Hyperbolic Tilings

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Re: Hyperbolic Tilings

Postby Marek14 » Thu Apr 02, 2015 5:43 pm

Well, this is as far as I've computed so far; a question now is, how to visualize these tilings?

There's Tyler, of course, but it's over 10 years old. It would be interesting to have a program with more advanced capabilities:

1. Computing and displaying the tilings automatically (my enumeration can serve as a base for selection of the tiling "types")
2. Support for colorings. For example, allow color selection for each type of polygon in the tiling and don't care whether the polygons are set to the same number of sides or different numbers.
3. Support for tilings including 2-gons, displayed as bold edges in specified color. Would work as long as there wouldn't be two 2-gons next to each other.
4. Panning the tiling, keeping the level of detail constant.
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Thu Apr 02, 2015 6:21 pm

Type ABABAC:

Edge data:
Code: Select all
b a c a b
a b A b a : A xH -D,B2

c a b a b
a b A c a : B1 xE1 -A

c a b a c
a b A b a : C xG -B1,C

b a b a b
a c A c a : D xF -A

b a b a c
a c A b a : B2 xE2 -B1,C

a c a b a
b a B a c : E1 xB1 -E1,F

a c a c a
b a B a b : F xD -G,E2

a b a b a
c a B a c : G xC -E1,F

a b a c a
c a B a b : E2 xB2 -G,E2

a b a b a
b a C a b : H xA -H


Vertex sequence:

A/H
H/A
D/F B2/E2
G/C E2/B2
B1/E1 C/G
E1/B1 F/D

16 possible sequences, leading to 4 basic solutions:

Solution 1: A/H-H/A-D/F-G/C-B1/E1-E1/B1 / A/H-H/A-B2/E2-E2/B2-C/G-F/D
1a: A'/H'-H/A-D/F-G/C-B1/E1-E1/B1 / A/H-H'/A'-B2/E2-E2/B2-C/G-F/D (AD,A'B2CB1|E1,E2,FG|HH')
1b: A/H-H/A-D/F-G/C-B1/E1-E1/B1 / A'/H'-H'/A'-B2/E2-E2/B2-C/G-F/D (ADA'B2CB1|E1,E2,FG|H,H')

Solution 2: A/H-H/A-D/F-G/C-C/G-F/D (AD,C|FG|H)

Solution 3: A/H-H/A-D/F-E2/B2-C/G-E1/B1 / A/H-H/A-B2/E2-G/C-B1/E1-F/D
3a: A'/H'-H/A-D/F-E2/B2-C/G-E1/B1 / A/H-H'/A'-B2/E2-G/C-B1/E1-F/D (AD,A'B2CB1|E1FE2G|HH')
3b: A/H-H/A-D/F-E2/B2-C/G-E1/B1 / A'/H'-H'/A'-B2/E2-G/C-B1/E1-F/D (ADA'B2CB1|E1FE2G|H,H')

Solution 4: A/H-H/A-B2/E2-E2/B2-B1/E1-E1/B1 (AB2B1|E1,E2|H)

2|a, 2|b: 2

3|a: 4

4|a, 2|b, 2|c: 1a
4|a, 4|b, 2|c: 3a

6|a, 2|b: 1b
6|a, 4|b: 3b
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Thu Apr 02, 2015 7:45 pm

Type AABBCC:

Edge data:
Code: Select all

b c c c b
b a A a b : A xO -E,C2

c b b b c
c a A a c : B xI -C1,D

c c a b b
b b A c c : C1 xC1 -A

c c a c c
b b A b b : D xE -B

b b a b b
c c A c c : E xD -A

b b a c c
c c A b b : C2 xC2 -B

c c b a a
a a B c c : F1 xF1 -H

c c b c c
a a B a a : G xJ -I

a c c c a
a b B b a : H xN -J,F2

c a a a c
c b B b c : I xB -F1,G

a a b a a
c c B c c : J xG -H

a a b c c
c c B a a : F2 xF2 -I

b b c a a
a a C b b : K1 xK1 -N

b b c b b
a a C a a : L xM -O

a a c a a
b b C b b : M xL -N

a a c b b
b b C a a : K2 xK2 -O

a b b b a
a c C c a : N xH -M,K2

a a a a b
b c C c b : O xA -K1,L


Vertex sequence:
A/O
K1/K1 L/M
N/H
J/G F2/F2
I/B
C1/C1 D/E

Reverse vertex sequence:
B/I
F1/F1 G/J
H/N
M/L K2/K2
O/A
E/D C2/C2

8 possible sequences, leading to 8 solutions:

Solution 1: A/O-K1/K1-N/H-J/G-I/B-C1/C1 / B/I-G/J-H/N-K2/K2-O/A-C2/C2 (AC2BC1|GI,HJ|K1NK2O)
Solution 2: A/O-K1/K1-N/H-J/G-I/B-D/E / B/I-G/J-H/N-K2/K2-O/A-E/D (AE,BD|GI,HJ|K1NK2O)
Solution 3: A/O-K1/K1-N/H-F2/F2-I/B-C1/C1 / B/I-F1/F1-H/N-K2/K2-O/A-C2/C2 (AC2BC1|F1HF2I|K1NK2O)
Solution 4: A/O-K1/K1-N/H-F2/F2-I/B-D/E / B/I-F1/F1-H/N-K2/K2-O/A-E/D (AE,BD|F1HF2I|K1NK2O)
Solution 5: A/O-L/M-N/H-J/G-I/B-C1/C1 / B/I-G/J-H/N-M/L-O/A-C2/C2 (AC2BC1|GI,HJ|LO,MN)
Solution 6: A/O-L/M-N/H-J/G-I/B-D/E / B/I-G/J-H/N-M/L-O/A-E/D (AE,BD|GI,HJ|LO,MN)
Solution 7: A/O-L/M-N/H-F2/F2-I/B-C1/C1 / B/I-F1/F1-H/N-M/L-O/A-C2/C2 (AC2BC1|F1HF2I|LO,MN)
Solution 8: A/O-L/M-N/H-F2/F2-I/B-D/E / B/I-F1/F1-H/N-M/L-O/A-E/D (AE,BD|F1HF2I|LO,MN)

Solutions 2, 5 and 8 are cognates and can be transformed into each other by switching a, b and c around. The same for solutions 1, 4 and 7

2|a, 2|b, 2|c - 6
2|a, 2|b, 4|c - 2
2|a, 4|b, 2|c - 8
2|a, 4|b, 4|c - 4

4|a, 2|b, 2|c - 5
4|a, 2|b, 4|c - 1
4|a, 4|b, 2|c - 7
4|a, 4|b, 4|c - 3
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Thu Apr 02, 2015 9:32 pm

Type AABCBC:

Edge data:
Code: Select all
c b c b c
b a A a b : A xS -E,C2

b c b c b
c a A a c : B xL -C1,D

b c a b c
c b A c b : C1 xC1 -A

b c a c b
c b A b c : D xE -B

c b a b c
b c A c b : E xD -A

c b a c b
b c A b c : C2 xC2 -B

c b c a a
a a B c b : F1 xM1 -I1,J,G2

c b c b a
a a B c a : G1 xP1 -K,I2,F2

c b c b c
a a B a a : H xR -L

a b c a a
a c B c b : I1 xN1 -I1,J,G2

a b c b a
a c B c a : J xQ -K,I2,F2

a b c b c
a c B a a : G2 xP2 -L

a a c a a
b c B c b : K xO -I1,J,G2

a a c b a
b c B c a : I2 xN2 -K,I2,F2

a a c b c
b c B a a : F2 xM2 -L

c a a a c
b c B c b : L xB -F1,G1,H

b c b a a
a a C b c : M1 xF1 -P1,Q,N2

b c b c a
a a C b a : N1 xI1 -R,P2,M2

b c b c b
a a C a a : O xK -S

a c b a a
a b C b c : P1 xG1 -P1,Q,N2

a c b c a
a b C b a : Q xJ -R,P2,M2

a c b c b
a b C a a : N2 xI2 -S

a a b a a
c b C b c : R xH -P1,Q,N2

a a b c a
c b C b a : P2 xG2 -R,P2,M2

a a b c b
c b C a a : M2 xF2 -S

b a a a b
c b C b c : S xA -M1,N1,O


Vertex sequence:
A/S
M1/F1 N1/I1 O/K
I1/N1 J/Q G2/P2
R/H P2/G2 M2/F2
L/B
C1/C1 D/E

Reverse vertex sequence:
B/L
F1/M1 G1/P1 H/R
P1/G1 Q/J N2/I2
K/O I2/N2 F2/M2
S/A
E/D C2/C2


54 possible sequences, leading to 8 solutions:

Solution 1: A/S-M1/F1-J/Q-M2/F2-L/B-C1/C1 / B/L-F1/M1-Q/J-F2/M2-S/A-C2/C2 (AC2BC1|F1JF2L|M1QM2S)
Solution 2: A/S-M1/F1-J/Q-M2/F2-L/B-D/E / B/L-F1/M1-Q/J-F2/M2-S/A-E/D (AE,BD|F1JF2L|M1QM2S)
Solution 3: A/S-N1/I1-I1/N1-R/H-L/B-C1/C1 / B/L-H/R-N2/I2-I2/N2-S/A-C2/C2 (AC2BC1|HL,I1,I2|N1RN2S)
Solution 4: A/S-N1/I1-I1/N1-R/H-L/B-D/E / B/L-H/R-N2/I2-I2/N2-S/A-E/D (AE,BD|HL,I1,I2|N1RN2S)
Solution 5: A/S-O/K-J/Q-R/H-L/B-C1/C1 / B/L-H/R-Q/J-K/O-S/A-C2/C2 (AC2BC1|HL,JK|OS,QR)
Solution 6: A/S-O/K-J/Q-R/H-L/B-D/E / B/L-H/R-Q/J-K/O-S/A-E/D (AE,BD|HL,JK|OS,QR)
Solution 7 (twin of solution 3): A/S-O/K-G2/P2-P2/G2-L/B-C1/C1 / B/L-G1/P1-P1/G1-K/O-S/A-C2/C2 (AC2BC1|G1KG2L|OS,P1,P2)
Solution 8 (twin of solution 4): A/S-O/K-G2/P2-P2/G2-L/B-D/E / B/L-G1/P1-P1/G1-K/O-S/A-E/D (AE,BD|G1KG2L|OS,P1,P2)

2|a, 2|b, 2|c: 6
2|a, 2|b, 4|c: 4
2|a, 4|b, 2|c: 8
2|a, 4|b, 4|c: 2

4|a, 2|b, 2|c: 5
4|a, 2|b, 4|c: 3
4|a, 4|b, 2|c: 7
4|a, 4|b, 4|c: 1
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Fri Apr 03, 2015 7:45 am

Three trivial types and one more complex:

Type AABCCB:

Edge data:
Code: Select all

c c b c c
b a A a b : A xD -B

c b a b c
c b A b c : B xB -A

b c c c b
a a B a a : C xF -D

b a a a b
c c B c c : D xA -C

a b c b a
a b C b a : E xE -F

a a b a a
b c C c b : F xC -E


Vertex sequence:
A/D
C/F
E/E
F/C
D/A
B/B

1 possible sequence, leading to 1 solution:

A/D-C/F-E/E-F/C-D/A-B/B (AB|CD|EF)

2|a, 2|b, 2|c

------

Type ABACBC:

Edge data:
Code: Select all
c b c b c
a b A b a : A xF -B

c a b a c
b c A c b : B xC -A

b c a c b
c a B a c : C xB -C

b a c a b
a c B c a : D xE -D

a c b c a
b a C a b : E xD -F

a b a b a
c b C b c : F xA -E


Vertex sequence:
A/F
E/D
D/E
F/A
B/C
C/B

1 possible sequence, leading to 1 solution:

A/F-E/D-D/E-F/A-B/C-C/B (AB|C,D|EF)

2|a, 2|c

------

Type ABCABC:

Edge data:
Code: Select all
a b c b a
c b A b c : A xF -B

a c b c a
b c A c b : B xD -A

b a c a b
c a B a c : C xE -D

b c a c b
a c B c a : D xB -C

c a b a c
b a C a b : E xC -F

c b a b c
a b C b a : F xA -E


Vertex sequence:
A/F
E/C
D/B
A/F
E/C
D/B

Reverse vertex sequence:
B/D
C/E
F/A
B/D
C/E
F/A

1 possible sequence, leading to 1 solution:

A/F-E/C-D/B-A/F-E/C-D/B / B/D-C/E-F/A-B/D-C/E-F/A (AB|CD|EF)

2|a, 2|b, 2|c

------

Type AAABCD:

Edge data:
Code: Select all
b c d c b
a a A a a : A xR -L,J2,G2,C2

d c b c d
a a A a a : B xN -J1,K,H2,D2

c d a a b
b a A d c : C1 xC1 -A

c d a a d
b a A b c : D1 xG1 -B

c d a b c
b a A a d : E1 xJ1 -C1,D1,E1,F

c d a d c
b a A a b : F xL -G1,H1,I,E2

c b a a b
d a A d c : G1 xD1 -A

c b a a d
d a A c b : H1 xH1 -B

c b a b c
d a A a d : I xK -C1,D1,E1,F

c b a d c
d a A a b : E2 xJ2 -G1,H1,I,E2

d a a a b
c b A d c : J1 xE1 -A

d a a a d
c b A b c : K xI -B

d a a b c
c b A a d : H2 xH2 -C1,D1,E1,F

d a a d c
c b A a b : D2 xG2 -G1,H1,I,E2

b a a a b
c d A d c : L xF -A

b a a a d
c d A b c : J2 xE2 -B

b a a b c
c d A a d : G2 xD2 -C1,D1,E1,F

b a a d c
c d A a b : C2 xC2 -G1,H1,I,E2

a d c d a
a a B a a : M xP -N

a a a a a
d c B c d : N xB -M

a a d a a
a b C b a : O xQ -P

a a b a a
a d C d a : P xM -O

a b c b a
a a D a a : Q xO -R

a a a a a
b c D c b : R xA -Q


Vertex sequence:
A/R
Q/O
P/M
N/B
J1/E1 K/I H2/H2 D2/G2
C1/C1 D1/G1 E1/J1 F/L

Reverse vertex sequence:
B/N
M/P
O/Q
R/A
L/F J2/E2 G2/D2 C2/C2
G1/D1 H1/H1 I/K E2/J2

16 possible sequences, leading to 6 solutions:

Solution 1: A/R-Q/O-P/M-N/B-J1/E1-E1/J1 / B/N-M/P-O/Q-R/A-J2/E2-E2/J2 (AJ2BJ1,E1,E2|MN|OP|QR)
Solution 2: A/R-Q/O-P/M-N/B-K/I-C1/C1 / B/N-M/P-O/Q-R/A-C2/C2-I/K (AC2IC1,BK|MN|OP|QR)
Solution 3: A/R-Q/O-P/M-N/B-K/I-F/L / B/N-M/P-O/Q-R/A-L/F-I/K (AL,BK,FI|MN|OP|QR)
Solution 4: A/R-Q/O-P/M-N/B-H2/H2-C1/C1 / B/N-M/P-O/Q-R/A-C2/C2-H1/H1 (AC2H1BH2C1|MN|OP|QR)
Solution 5 (twin of solution 2): A/R-Q/O-P/M-N/B-H2/H2-F/L / B/N-M/P-O/Q-R/A-L/F-H1/H1 (AL,BH2FH1|MN|OP|QR)
Solution 6: A/R-Q/O-P/M-N/B-D2/G2-D1/G1 / B/N-M/P-O/Q-R/A-G2/D2-G1/D1 (AG2D1BD2G1|MN|OP|QR)

2|a, 2|b, 2|c, 2|d: 3

4|a, 2|b, 2|c, 2|d: 1, 2, 5

6|a, 2|b, 2|c, 2|d: 4, 6
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Fri Apr 03, 2015 8:11 am

Type AABACD:

Edge data:
Code: Select all
a c d c a
b a A a b : A xO -H,E2

c a b a a
d a A c d : B1 xI1 -D

c a b a c
d a A a d : C xK -E1,F

a d c d a
a b A b a : D xM -G,B2

c d a b a
a b A d c : E1 xE1 -A

c d a d c
a b A b a : F xH -B1,C

a a b a a
d c A c d : G xJ -D

a a b a c
d c A a d : B2 xI2 -E1,F

a b a b a
c d A d c : H xF -A

a b a d c
c d A b a : E2 xE2 -B1,C

d c a a d
a a B a c : I1 xB1 -I1,J

d c a c d
a a B a a : J xG -K,I2

d a a a d
c a B a c : K xC -I1,J

d a a c d
c a B a a : I2 xB2 -K,I2

a a d a a
b a C a b : L xN -M

a b a b a
a d C d a : M xD -L

b a c a b
a a D a a : N xL -O

b a a a b
a c D c a : O xA -N


Vertex sequence:
A/O
N/L
M/D
G/J B2/I2
K/C I2/B2
E1/E1 F/H

Reverse vertex sequence:
B1/I1 C/K
I1/B1 J/G
D/M
L/N
O/A
H/F E2/E2

8 possible sequences, leading to 4 solutions:

Solution 1: A/O-N/L-M/D-G/J-K/C-E1/E1 / C/K-J/G-D/M-L/N-O/A-E2/E2 (AE2CE1,DG|JK|LM|NO)
Solution 2: A/O-N/L-M/D-G/J-K/C-F/H / C/K-J/G-D/M-L/N-O/A-H/F (AH,CF,DG|JK|LM|NO)
Solution 3: A/O-N/L-M/D-B2/I2-I2/B2-E1/E1 / B1/I1-I1/B1-D/M-L/N-O/A-E2/E2 (AE2B1DB2E1|I1,I2|LM|NO)
Solution 4: A/O-N/L-M/D-B2/I2-I2/B2-F/H / B1/I1-I1/B1-D/M-L/N-O/A-H/F (AH,B1DB2F|I1,I2|LM|NO)

2|a, 2|b, 2|c, 2|d: 2

4|a, 2|c, 2|d: 4
4|a, 2|b, 2|c, 2|d: 1

6|a, 2|c, 2|d: 3
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Fri Apr 03, 2015 10:23 am

Type ABACAD:

Edge data:
Code: Select all
c a d a b
a b A c a : A1 xP1 -H,C2

c a d a c
a b A b a : B xR -I,F2

d a c a b
a b A d a : C1 xM1 -E,A2

d a c a d
a b A b a : D xO -F1,G

b a d a b
a c A c a : E xQ -H,C2

b a d a c
a c A b a : A2 xP2 -I,F2

d a b a c
a c A d a : F1 xJ1 -A1,B

d a b a d
a c A c a : G xL -C1,D

b a c a b
a d A d a : H xN -E,A2

b a c a d
a d A b a : C2 xM2 -F1,G

c a b a c
a d A d a : I xK -A1,B

c a b a d
a d A c a : F2 xJ2 -C1,D

a d a c a
c a B a d : J1 xF1 -J1,K

a d a d a
c a B a c : K xI -L,J2

a c a c a
d a B a d : L xG -J1,K

a c a d a
d a B a c : J2 xF2 -L,J2

a d a b a
b a C a d : M1 xC1 -M1,N

a d a d a
b a C a b : N xH -O,M2

a b a b a
d a C a d : O xD -M1,N

a b a d a
d a C a b : M2 xC2 -O,M2

a c a b a
b a D a c : P1 xA1 -P1,Q

a c a c a
b a D a b : Q xE -R,P2

a b a b a
c a D a c : R xB -P1,Q

a b a c a
c a D a b : P2 xA2 -R,P2


Vertex sequence:
A1/P1 B/R
P1/A1 Q/E
H/N C2/M2
O/D M2/C2
F1/J1 G/L
J1/F1 K/I

Reverse vertex sequence:
C1/M1 D/O
M1/C1 N/H
E/Q A2/P2
R/B P2/A2
I/K F2/J2
L/G J2/F2

64 possible sequences, leading to 8 solutions:

Solution 1: A1/P1-P1/A1-H/N-O/D-F1/J1-J1/F1 / D/O-N/H-A2/P2-P2/A2-F2/J2-J2/F2 (A1HA2F2DF1|J1,J2|NO|P1,P2)
Solution 2: A1/P1-P1/A1-H/N-O/D-G/L-K/I / D/O-N/H-A2/P2-P2/A2-I/K-L/G (A1HA2I,DG|KL|NO|P1,P2)
Solution 3 (chiral): A1/P1-P1/A1-C2/M2-M2/C2-F1/J1-J1/F1 / C1/M1-M1/C1-A2/P2-P2/A2-F2/J2-J2/F2 (A1C2F1|J1|M2|P1)/(C1A2F2|J2|M1|P2)
Solution 4: A1/P1-P1/A1-C2/M2-M2/C2-G/L-K/I / C1/M1-M1/C1-A2/P2-P2/A2-I/K-L/G (A1C2GC1A2I|KL|M1,M2|P1,P2)
Solution 5: B/R-Q/E-H/N-O/D-F1/J1-J1/F1 / D/O-N/H-E/Q-R/B-F2/J2-J2/F2 (BF2DF1,EH|J1,J2|NO|RQ)
Solution 6: B/R-Q/E-H/N-O/D-G/L-K/I / D/O-N/H-E/Q-R/B-I/K-L/G (BI,DG,EH|KL|NO|RQ)
Solution 7: B/R-Q/E-C2/M2-M2/C2-F1/J1-J1/F1 / C1/M1-M1/C1-E/Q-R/B-F2/J2-J2/F2 (BF2C1EC2F1|J1,J2|M1,M2|RQ)
Solution 8: B/R-Q/E-C2/M2-M2/C2-G/L-K/I / C1/M1-M1/C1-E/Q-R/B-I/K-L/G (BI,C1EC2G|KL|M1,M2|RQ)

Solutions 1, 4 and 7 are cognates, as well as solutions 2, 5 and 8.

2|a, 2|b, 2|c, 2|d: 6

3|a: 3

4|a, 2|b, 2|c: 2
4|a, 2|b, 2|d: 8
4|a, 2|c, 2|d: 5

6|a, 2|b: 4
6|a, 2|c: 1
6|a, 2|d: 7
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby wendy » Fri Apr 03, 2015 11:51 am

What are ye making your solutions in? Tyler? It's dizzingly fast.
The dream you dream alone is only a dream
the dream we dream together is reality.
User avatar
wendy
Pentonian
 
Posts: 1846
Joined: Tue Jan 18, 2005 12:42 pm
Location: Brisbane, Australia

Re: Hyperbolic Tilings

Postby Marek14 » Fri Apr 03, 2015 2:28 pm

Type AABBCD:

Edge data:
Code: Select all
b c d c b
b a A a b : A xN -E,C2

c b b b c
d a A a d : B xI -C1,D

c d a b b
b b A d c : C1 xC1 -A

c d a d c
b b A b b : D xE -B

b b a b b
c d A d c : E xD -A

b b a d c
c d A b b : C2 xC2 -B

d c b a a
a a B c d : F1 xF1 -H

d c b c d
a a B a a : G xJ -I

a d c d a
a b B b a : H xL -J,F2

d a a a d
c b B b c : I xB -F1,G

a a b a a
d c B c d : J xG -H

a a b c d
d c B a a : F2 xF2 -I

a a d a a
b b C b b : K xM -L

a b b b a
a d C d a : L xH -K

b b c b b
a a D a a : M xK -N

b a a a b
b c D c b : N xA -M


Vertex sequence:
A/N
M/K
L/H
J/G F2/F2
I/B
C1/C1 D/E

Reverse vertex sequence:
B/I
F1/F1 G/J
H/L
K/M
N/A
E/D C2/C2

4 possible sequences, leading to 4 solutions:

Solution 1: A/N-M/K-L/H-J/G-I/B-C1/C1 / B/I-G/J-H/L-K/M-N/A-C2/C2 (AC2BC1|GI,HJ|KL|MN)
Solution 2: A/N-M/K-L/H-J/G-I/B-D/E / B/I-G/J-H/L-K/M-N/A-E/D (AE,BD|GI,HJ|KL|MN)
Solution 3: A/N-M/K-L/H-F2/F2-I/B-C1/C1 / B/I-F1/F1-H/L-K/M-N/A-C2/C2 (AC2BC1|F1HF2I|KL|MN)
Solution 4 (twin of solution 1): A/N-M/K-L/H-F2/F2-I/B-D/E / B/I-F1/F1-H/L-K/M-N/A-E/D (AE,BD|F1HF2I|KL|MN)

2|a, 2|b, 2|c, 2|d: 2
2|a, 4|b, 2|c, 2|d: 4

4|a, 2|b, 2|c, 2|d: 1
4|a, 4|b, 2|c, 2|d: 3
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sat Apr 04, 2015 7:09 am

Type AABCBD:

Edge data:
Code: Select all
c b d b c
b a A a b : A xO -E,C2

b c b c b
d a A a d : B xI -C1,D

b d a b c
c b A d b : C1 xC1 -A

b d a d b
c b A b c : D xE -B

c b a b c
b d A d b : E xD -A

c b a d b
b d A b c : C2 xC2 -B

d b c b a
a a B d a : F1 xK1 -H

d b c b d
a a B a a : G xM -I

a a d a a
b c B c b : H xN -J,F2

d a a a d
b c B c b : I xB -F1

a b c b a
a d B d a : J xL -G,H

a b c b d
a d B a a : F2 xK2 -G,H

a d b a a
a b C b d : K1 xF1 -K1,L

a d b d a
a b C b a : L xJ -M,K2

a a b a a
d b C b d : M xG -K1,L

a a b d a
d b C b a : K2 xF2 -M,K2

b c b c b
a a D a a : N xH -O

b a a a b
c b D b c : O xA -N


Vertex sequence:
A/O
N/H
J/L F2/K2
M/G K2/F2
I/B
C1/C1 D/E

Reverse vertex sequence:
B/I
F1/K1 G/M
K1/F1 L/J
H/N
O/A
E/D C2/C2

8 possible sequences, leading to 4 solutions:

Solution 1: A/O-N/H-J/L-M/G-I/B-C1/C1 / B/I-G/M-L/J-H/N-O/A-C2/C2 (AC2BC1|GI,HJ|LM|NO)
Solution 2: A/O-N/H-J/L-M/G-I/B-D/E / B/I-G/M-L/J-H/N-O/A-E/D (AE,BD|GI,HJ|LM|NO)
Solution 3: A/O-N/H-F2/K2-K2/F2-I/B-C1/C1 / B/I-F1/K1-K1/F1-H/N-O/A-C2/C2 (AC2BC1|F1HF2I|K1,K2|NO)
Solution 4: A/O-N/H-F2/K2-K2/F2-I/B-D/E / B/I-F1/K1-K1/F1-H/N-O/A-E/D (AE,BD|F1HF2I|K1,K2|NO)

2|a, 2|b, 2|c, 2|d: 2
2|a, 4|b, 2|d: 4

4|a, 2|b, 2|c, 2|d: 1
4|a, 4|b, 2|d: 3
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sat Apr 04, 2015 12:21 pm

Type AABCDB:

Edge data:
Code: Select all
c d b c d
b a A a b : A1 xI1 -D1,E

c d b d c
b a A a b : B xK -F,D2

d c b c d
b a A a b : C xJ -D1,E

d c b d c
b a A a b : A2 xI2 -F,D2

d b a b c
c b A b d : D1 xD1 -A1,B

d b a b d
c b A b c : E xF -C,A2

c b a b c
d b A b d : F xE -A1,B

c b a b d
d b A b c : D2 xD2 -C,A2

b c d c b
a a B a a : G xO -K,I2

b d c d b
a a B a a : H xM -I1,J

b a a a b
d c B d c : I1 xA1 -G

b a a a b
d c B c d : J xC -H

b a a a b
c d B d c : K xB -G

b a a a b
c d B c d : I2 xA2 -H

a b d b a
a b C b a : L xN -M

a a b a a
b d C d b : M xH -L

a b c b a
a b D b a : N xL -O

a a b a a
b c D c b : O xD -N


Vertex sequence:
A1/I1 B/K
G/O
N/L
M/H
I1/A1 J/C
D1/D1 E/F

Reverse vertex sequence:
C/J A2/I2
H/M
L/N
O/G
K/B I2/A2
F/E D2/D2

8 possible sequences, leading to 4 solutions:

Solution 1: A1/I1-G/O-N/L-M/H-I1/A1-D1/D1 | A2/I2-H/M-L/N-O/G-I2/A2-D2/D2 (A1D1,A2D2|GI2HI1|LM|NO)
Solution 2: A1/I1-G/O-N/L-M/H-I1/A1-E/F | A2/I2-H/M-L/N-O/G-I2/A2-F/E (A1EA2F|GI2HI1|LM|NO)
Solution 3: B/K-G/O-N/L-M/H-J/C-D1/D1 | C/J-H/M-L/N-O/G-K/B-D2/D2 (BD2CD1|GK,HJ|LM|NO)
Solution 4: B/K-G/O-N/L-M/H-J/C-E/F | C/J-H/M-L/N-O/G-K/B-F/E (BF,CE|GK,HJ|LM|NO)

2|a, 2|b, 2|c, 2|d: 4
2|a, 4|b, 2|c, 2|d: 1

4|a, 2|b, 2|c, 2|d: 3
4|a, 4|b, 2|c, 2|d: 2
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sat Apr 04, 2015 2:28 pm

Type AACBBD:

Edge data:
Code: Select all
b b d b b
c a A a c : A xO -E,C2

b b c b b
d a A a d : B xM -C1,D

b d a c b
b c A d b : C1 xC1 -A

b d a d b
b c A c b : D xE -B

b c a c b
b d A d b : E xD -A

b c a d b
b d A c b : C2 xC2 -B

a a d a a
c b B b c : F xN -J,H2

a a c a a
d b B d b : G xL -H1,I

a d b c a
a c B d a : H1 xH1 -F

a d b d a
a c B c a : I xJ -G

a c b c a
a d B d a : J xI -F

a c b d a
a d B c a : H2 xH2 -G

d b b b d
a a C a a : L xG -M

d a a a d
b b C b b : M xB -L

c b b b c
a a D a a : N xF -O

c a a a c
b b D b b : O xA -N


Vertex sequence:
A/O
N/F
J/I H2/H2
G/L
M/B
C1/C1 D/E

Reverse vertex sequence:
B/M
L/G
H1/H1 I/J
F/N
O/A
E/D C2/C2

4 possible sequences, leading to 4 solutions:

Solution 1: A/O-N/F-J/I-G/L-M/B-C1/C1 | B/M-L/G-I/J-F/N-O/A-C2/C2 (AC2BC1|FJ,GI|LM|NO)
Solution 2: A/O-N/F-J/I-G/L-M/B-D/E | B/M-L/G-I/J-F/N-O/A-E/D (AE,BD|FJ,GI|LM|NO)
Solution 3: A/O-N/F-H2/H2-G/L-M/B-C1/C1 | B/M-L/G-H1/H1-F/N-O/A-C2/C2 (AC2BC1|FH2GH1|LM|NO)
Solution 4 (twin of solution 1): A/O-N/F-H2/H2-G/L-M/B-D/E | B/M-L/G-H1/H1-F/N-O/A-E/D (AE,BD|FH2GH1|LM|NO)

2|a, 2|b, 2|c, 2|d: 2
2|a, 4|b, 2|c, 2|d: 4

4|a, 2|b, 2|c, 2|d: 1
4|a, 4|b, 2|c, 2|d: 3
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sun Apr 05, 2015 8:56 am

Type ABABCD:

Edge data:
Code: Select all
b c d c b
a b A b a : A xR -G,E2,B2

d c b a b
a b A d c : B1 xI1 -A

d c b a d
a b A b c : C1 xL1 -B1,C1,D

d c b c d
a b A b a : D xN -E1,F,C2

d a b a b
c b A d c : E1 xJ1 -A

d a b a d
c b A b c : F xM -B1,C1,D

d a b c d
c b A b a : C2 xL2 -E1,F,C2

b a b a b
c d A d c : G xK -A

b a b a d
c d A b c : E2 xJ2 -B1,C1,D

b a b c d
c d A b a : B2 xI2 -E1,F,C2

a d c d a
b a B a b : H xP -N,L2,I2

c d a b a
b a B c d : I1 xB1 -H

c d a b c
b a B a d : J1 xE1 -I1,J1,K

c d a d c
b a B a b : K xG -L1,M,J2

c b a b a
d a B c d : L1 xC1 -H

c b a b c
d a B a d : M xF -I1,J1,K

c b a d c
d a B a b : J2 xE2 -L1,M,J2

a b a b a
d c B c d : N xD -H

a b a b c
d c B a d : L2 xC2 -I1,J1,K

a b a d c
d c B a b : I2 xB2 -L1,M,J2

b a d a b
a b C b a : O xQ -P

b a b a b
a d C d a : P xH -O

a b c b a
b a D a b : Q xO -R

a b a b a
b c D c b : R xA -Q


Vertex sequence:
A/R
Q/O
P/H
N/D L2/C2 I2/B2
E1/J1 F/M C2/L2
I1/B1 J1/E1 K/G

Reverse vertex sequence:
B1/I1 C1/L1 D/N
H/P
O/Q
R/A
G/K E2/J2 B2/I2
L1/C1 M/F J2/E2

27 possible sequences, leading to 4 solutions:

Solution 1: A/R-Q/O-P/H-N/D-E1/J1-J1/E1 | D/N-H/P-O/Q-R/A-E2/J2-J2/E2 (AE2DE1|HN,J1,J2|OP|QR)
Solution 2: A/R-Q/O-P/H-N/D-F/M-K/G | D/N-H/P-O/Q-R/A-G/K-M/F (AG,DF|HN,KM|OP|QR)
Solution 3 (twin of solution 1): A/R-Q/O-P/H-L2/C2-C2/L2-K/G | C1/L1-H/P-O/Q-R/A-G/K-L1/C1 (AG,C1,C2|HL2KL1|OP|QR)
Solution 4: A/R-Q/O-P/H-I2/B2-F/M-I1/B1 | B1/I1-H/P-O/Q-R/A-B2/I2-M/F (AB2FB1|HI2MI1|OP|QR)

2|a, 2|b, 2|c, 2|d: 2
2|a, 4|b, 2|c, 2|d: 3

4|a, 2|b, 2|c, 2|d: 1
4|a, 4|b, 2|c, 2|d: 4
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sun Apr 05, 2015 12:07 pm

Type ABACBD:

Edge data:
Code: Select all
c b d b c
a b A b a : A xN -E,C2

d b c b d
a b A b a : B xL -C1,D

d a b a c
b c A d b : C1 xF1 -A

d a b a d
b c A c b : D xH -B

c a b a c
b d A d b : E xG -A

c a b a d
b d A c b : C2 xF2 -B

b d a c b
c a B a d : F1 xC1 -F1,G

b d a d b
c a B a c : G xE -H,F2

b c a c b
d a B a d : H xD -F1,G

b c a d b
d a B a c : F2 xC2 -H,F2

b a d a b
a c B c a : I xM -J

b a c a b
a d B d a : J xK -I

a d b d a
b a C a b : K xJ -L

a b a b a
d b C b d : L xB -K

a c b c a
b a D a b : M xI -N

a b a b a
c b D b c : N xA -M


Vertex sequence:
A/N
M/I
J/K
L/B
C1/F1 D/H
F1/C1 G/E

Reverse vertex sequence:
B/L
K/J
I/M
N/A
E/G C2/F2
H/D F2/C2

4 possible sequences, leading to 2 solutions:

Solution 1: A/N-M/I-J/K-L/B-C1/F1-F1/C1 | B/L-K/J-I/M-N/A-C2/F2-F2/C2 (AC2BC1|F1,F2,IJ|KL|MN)
Solution 2: A/N-M/I-J/K-L/B-D/H-G/E | B/L-K/J-I/M-N/A-E/G-H/D (AE,BD|GH,IJ|KL|MN)

2|a, 2|b, 2|c, 2|d: 2

4|a, 2|b, 2|c, 2|d: 1
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sun Apr 05, 2015 12:28 pm

Type ABCBAD:

Edge data:
Code: Select all
b a d a b
c b A b c : A xF -B

b c b c b
a d A d a : B xD -A

a b c b a
d a B a d : C xE -D

a d a d a
b c B c b : D xB -C

d a b a d
a b C b a : E xC -E

c b a b c
b a D a d : F xA -F


Single solution:

A/F-F/A-B/D-C/E-E/C-D/B (AB|CD|E|F)

2|a, 2|b

------

Type ABCABD:

Edge data:
Code: Select all
a b d b a
c b A b c : A xN -E,C2

a b c b a
d b A b d : B xL -C1,D

a d b c a
b c A d b : C1 xH1 -A

a d b d a
b c A c b : D xJ -B

a c b c a
b d A d b : E xI -A

a c b d a
b d A c b : C2 xH2 -B

b a d a b
c a B a c : F xM -J,H2

b a c a b
d a B a d : G xK -H1,I

b d a c b
a c B d a : H1 xC1 -F

b d a d b
a c B c a : I xE -G

b c a c b
a d B d a : J xD -F

b c a d b
a d B c a : H2 xC2 -G

d a b a d
b a C a b : K xG -L

d b a b d
a b C b a : L xB -K

c a b a c
b a D a b : M xF -N

c b a b c
a b D b a : N xA -M


Vertex sequence:
A/N
M/F
J/D H2/C2
B/L
K/G
H1/C1 I/E

Reverse vertex sequence:
C1/H1 D/J
F/M
N/A
E/I C2/H2
G/K
L/B

4 possible sequences, leading to 2 solutions:

Solution 1: A/N-M/F-J/D-B/L-K/G-I/E | D/J-F/M-N/A-E/I-G/K-L/B (AE,BD|FJ,GI|KL|MN)
Solution 2: A/N-M/F-H2/C2-B/L-K/G-H1/C1 | C1/H1-F/M-N/A-C2/H2-G/K-L/B (AC2BC1|FH2GH1|KL|MN)

2|a, 2|b, 2|c, 2|d: 1
4|a, 4|b, 2|c, 2|d: 2
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sun Apr 05, 2015 12:48 pm

Type AABCDE:

Edge data:
Code: Select all
c d e d b
b a A a c : A xM -E,C2

d c b c d
e a A a e : B xG -C1,D

d e a b c
c b A e d : C1 xC1 -A

d e a e d
c b A b c : D xE -B

c b a b c
d e A e d : E xD -A

c b a e d
d e A b c : C2 xC2 -B

e d c d e
a a B a a : F xI -G

e a a a e
d c B c d : G xB -F

a e d e a
a b C a b : H xK -I

a a b a a
e d C d e : I xF -H

a a e a a
b c D c b : J xL -K

a b c b a
a e D e a : K xH -J

b c d c b
a a E a a : L xJ -M

b a a a b
c d E d c : M xA -L


Vertex sequence:
A/M
L/J
K/H
I/F
G/B
C1/C1 D/E

Reverse vertex sequence:
B/G
F/I
H/K
J/L
M/A
E/D C2/C2

2 possible sequences, leading to 2 solutions:

Solution 1: A/M-L/J-K/H-I/F-G/B-C1/C1 | B/G-F/I-H/K-J/L-M/A-C2/C2 (AC2BC1|FG|HI|JK|LM)
Solution 2: A/M-L/J-K/H-I/F-G/B-D/E | B/G-F/I-H/K-J/L-M/A-E/D (AE,BD|FG|HI|JK|LM)

2|a, 2|b, 2|c, 2|d, 2|e: 2

4|a, 2|b, 2|c, 2|d, 2|e: 1
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sun Apr 05, 2015 1:00 pm

Type ABACDE:

Edge data:
Code: Select all
c d e d c
a b A b a : A xN -E,C2

e d c d e
a b A b a : B xJ -C1,D

e a b a c
d c A e d : C1 xF1 -A

e a b a e
d c A c d : D xH -B

c a b a c
d e A e d : E xG -A

c a b a e
d e A c d : C2 xF2 -B

d e a c d
c a B a e : F1 xC1 -F1,G

d e a e d
c a B a c : G xE -H,F2

d c a c d
e a B a e : H xD -F1,G

d c a e d
e a B a c : F2 xC2 -H,F2

a e d e a
b a C a b : I xL -J

a b a b a
e d C d e : J xB -I

b a e a b
a c D c a : K xM -L

b a c a b
a e D e a : L xI -K

a c d c a
b a E a b : M xK -N

a b a b a
c d E d c : N xA -M


Vertex sequence:
A/N
M/K
L/I
J/B
C1/F1 D/H
F1/C1 G/E

Reverse vertex sequence:
B/J
I/L
K/M
N/A
E/G C2/F2
H/D F2/C2

4 possible sequences, leading to 2 solutions:

Solution 1: A/N-M/K-L/I-J/B-C1/F1-F1/C1 | B/J-I/L-K/M-N/A-C2/F2-F2/C2 (AC2BC1|F1,F2|IJ|KL|MN)
Solution 2: A/N-M/K-L/I-J/B-D/H-G/E | B/J-I/L-K/M-N/A-E/G-H/D (AE,BD|GH|IJ|KL|MN)

2|a, 2|b, 2|c, 2|d, 2|e: 2

4|a, 2|c, 2|d, 2|e: 1
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sun Apr 05, 2015 1:33 pm

Type ABCADE:

Edge data:
Code: Select all
a d e d a
c b A b c : A xL -D

a e d e a
b c A c b : B xJ -C

a b c b a
e d A d e : C xH -B

a c b c a
d e A e d : D xF -A

d a c a d
e a B a e : E xG -F

d e a e d
a c B c a : F xD -E

e a b a e
d a C a d : G xE -H

e d a d e
a b C b a : H xC -G

b a e a b
c a D a c : I xK -J

b c a c b
a e D e a : J xB -I

c a d a c
b a E a b : K xI -L

c b a b c
a d E d a : L xA -K


Single solution:

A/L-K/I-J/B-C/H-G/E-F/D | B/J-I/K-L/A-D/F-E/G-H/C (AD,BC|EF|GH|IJ|KL)

2|a, 2|b, 2|c, 2|d, 2|e

------

Type ABCDEF:

Edge data:
Code: Select all
d e f e d
c b A b c : A xL -B

d c b c d
e f A f e : B xD -A

e d c d e
f a B a f : C xF -D

e f a f e
d c B c d : D xB -C

f e d e f
a b C b a : E xH -F

f a b a f
e d C d e : F xC -E

a f e f a
b c D c b : G xJ -H

a b c b a
f e D e f : H xE -G

b a f a b
c d E d c : I xK -J

b c d c b
a f E f a : J xG -I

c d e d c
b a F a b : K xI -L

c b a b c
d e F e d : L xA -K


Single solution:

A/L-K/I-J/G-H/E-F/C-D/B | B/D-C/F-E/H-G/J-I/K-L/A (AB|CD|EF|GH|IJ|KL)

2|a, 2|b, 2|c, 2|d, 2|e, 2|f

And this, my friends, should be all the 6-valent tilings.
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sun Apr 05, 2015 9:14 pm

Type AAAAAAB:

Edge data:
Code: Select all
a a b a a
a       a
a a A a a : A xQ -P,N2,K2,G2,B2

a b a a a
a       a
a a A b a : B1 xB1 -A

a b a a a
a       a
a a A a b : C1 xG1 -B1,C1,D1,E1,F

a b a a a
a       b
a a A a a : D1 xK1 -G1,H1,I1,J,E2

a b a a b
a       a
a a A a a : E1 xN1 -K1,L1,M,I2,D2

a b a b a
a       a
a a A a a : F xP -N1,O,L2,H2,C2

b a a a a
a       a
a a A b a : G1 xC1 -A

b a a a a
a       a
a a A a b : H1 xH1 -B1,C1,D1,E1,F

b a a a a
a       b
a a A a a : I1 xL1 -G1,H1,I1,J,E2

b a a a b
a       a
a a A a a : J xO -K1,L1,M,I2,D2

b a a b a
a       a
a a A a a : E2 xN2 -N1,O,L2,H2,C2

a a a a a
b       a
a a A b a : K1 xD1 -A

a a a a a
b       a
a a A a b : L1 xI1 -B1,C1,D1,E1,F

a a a a a
b       b
a a A a a : M xM -G1,H1,I1,J,E2

a a a a b
b       a
a a A a a : I2 xL2 -K1,L1,M,I2,D2

a a a b a
b       a
a a A a a : D2 xK2 -N1,O,L2,H2,C2

a a a a a
a       a
b a A b a : N1 xE1 -A

a a a a a
a       a
b a A a b : O xJ -B1,C1,D1,E1,F

a a a a a
a       b
b a A a a : L2 xI2 -G1,H1,I1,J,E2

a a a a b
a       a
b a A a a : H2 xH2 -K1,L1,M,I2,D2

a a a b a
a       a
b a A a a : C2 xG2 -N1,O,L2,H2,C2

a a a a a
a       a
a b A b a : P xF -A

a a a a a
a       a
a b A a b : N2 xE2 -B1,C1,D1,E1,F

a a a a a
a       b
a b A a a : K2 xD2 -G1,H1,I1,J,E2

a a a a b
a       a
a b A a a : G2 xC2 -K1,L1,M,I2,D2

a a a b a
a       a
a b A a a : B2 xB2 -N1,O,L2,H2,C2

a a a a a
a       a
a a B a a : Q xA -Q


Vertex sequence:
A/Q
Q/A
P/F N2/E2 K2/D2 G2/C2 B2/B2
N1/E1 O/J L2/I2 H2/H2 C2/G2
K1/D1 L1/I1 M/M I2/L2 D2/K2
G1/C1 H1/H1 I1/L1 J/O E2/N2
B1/B1 C1/G1 D1/K1 E1/N1 F/P

3125 possible sequences, leading to 94 basic solutions:

Solution 1: A/Q-Q/A-P/F-N1/E1-L1/I1-I1/L1-E1/N1 | A/Q-Q/A-N2/E2-L2/I2-I2/L2-E2/N2-F/P
1a: A'/Q'-Q/A-P/F-N1/E1-L1/I1-I1/L1-E1/N1 | A/Q-Q'/A'-N2/E2-L2/I2-I2/L2-E2/N2-F/P (AP,A'N2FN1,E1L1,I1,E2L2,I2|QQ')
1b: A/Q-Q/A-P/F-N1/E1-L1/I1-I1/L1-E1/N1 | A'/Q'-Q'/A'-N2/E2-L2/I2-I2/L2-E2/N2-F/P (APA'N2FN1,E1L1,I1,E2L2,I2|Q,Q')

Solution 2: A/Q-Q/A-P/F-N1/E1-M/M-H1/H1-E1/N1 | A/Q-Q/A-N2/E2-H2/H2-M/M-E2/N2-F/P
2a: A'/Q'-Q/A-P/F-N1/E1-M/M'-H1/H1-E1/N1 | A/Q-Q'/A'-N2/E2-H2/H2-M'/M-E2/N2-F/P (AP,A'N2FN1,E1ME2H2M'H1|QQ')
2b: A'/Q'-Q/A-P/F-N1/E1-M/M-H1/H1-E1/N1 | A/Q-Q'/A'-N2/E2-H2/H2-M'/M'-E2/N2-F/P (AP,A'N2FN1,E1MH1,E2H2M'|QQ')
2c: A/Q-Q/A-P/F-N1/E1-M/M'-H1/H1-E1/N1 | A'/Q'-Q'/A'-N2/E2-H2/H2-M'/M-E2/N2-F/P (APA'N2FN1,E1ME2H2MH1|Q,Q')
2d: A/Q-Q/A-P/F-N1/E1-M/M-H1/H1-E1/N1 | A'/Q'-Q'/A'-N2/E2-H2/H2-M'/M'-E2/N2-F/P (APA'N2FN1,E1MH1,E2H2M'|Q,Q')

Solution 3: A/Q-Q/A-P/F-N1/E1-M/M-J/O-E1/N1 | A/Q-Q/A-N2/E2-O/J-M/M-E2/N2-F/P
3a: A'/Q'-Q/A-P/F-N1/E1-M/M'-J/O-E1/N1 | A/Q-Q'/A'-N2/E2-O/J-M'/M-E2/N2-F/P (AP,A'N2FN1,E1ME2O,JM'|QQ')
3b: A'/Q'-Q/A-P/F-N1/E1-M/M-J/O-E1/N1 | A/Q-Q'/A'-N2/E2-O/J-M'/M'-E2/N2-F/P (AP,A'N2FN1,E1MJM'E2O|QQ')
3c: A/Q-Q/A-P/F-N1/E1-M/M'-J/O-E1/N1 | A'/Q'-Q'/A'-N2/E2-O/J-M'/M-E2/N2-F/P (APA'N2FN1,E1ME2O,JM'|Q,Q')
3d: A/Q-Q/A-P/F-N1/E1-M/M-J/O-E1/N1 | A'/Q'-Q'/A'-N2/E2-O/J-M'/M'-E2/N2-F/P (APA'N2FN1,E1MJM'E2O|Q,Q')

Solution 4: A/Q-Q/A-P/F-N1/E1-I2/L2-I1/L1-E1/N1 | A/Q-Q/A-N2/E2-L2/I2-L1/I1-E2/N2-F/P
4a: A'/Q'-Q/A-P/F-N1/E1-I2/L2-I1/L1-E1/N1 | A/Q-Q'/A'-N2/E2-L2/I2-L1/I1-E2/N2-F/P (AP,A'N2FN1,E1I2L1,I1E2L2|QQ')
4b: A/Q-Q/A-P/F-N1/E1-I2/L2-I1/L1-E1/N1 | A'/Q'-Q'/A'-N2/E2-L2/I2-L1/I1-E2/N2-F/P (APA'N2FN1,E1I2L1,I1E2L2|Q,Q')

Solution 5: A/Q-Q/A-P/F-O/J-K1/D1-H1/H1-D1/K1 | A/Q-Q/A-K2/D2-H2/H2-D2/K2-J/O-F/P
5a: A'/Q'-Q/A-P/F-O/J-K1/D1-H1/H1-D1/K1 | A/Q-Q'/A'-K2/D2-H2/H2-D2/K2-J/O-F/P (AP,A'K2JK1,D1H1,FO,D2H2|QQ')
5b: A/Q-Q/A-P/F-O/J-K1/D1-H1/H1-D1/K1 | A'/Q'-Q'/A'-K2/D2-H2/H2-D2/K2-J/O-F/P (APA'K2JK1,D1H1,FO,D2H2|Q,Q')

Solution 6: A/Q-Q/A-P/F-O/J-K1/D1-J/O-D1/K1 | A/Q-Q/A-K2/D2-O/J-D2/K2-J/O-F/P
6a: A'/Q'-Q/A-P/F-O/J-K1/D1-J'/O'-D1/K1 | A/Q-Q'/A'-K2/D2-O'/J'-D2/K2-J/O-F/P (AP,A'K2JK1,D1J'D2O',FO|QQ')
6b: A'/Q'-Q/A-P/F-O'/J'-K1/D1-J'/O'-D1/K1 | A/Q-Q'/A'-K2/D2-O/J-D2/K2-J/O-F/P (AP,A'K2JD2OFO'D1J'K1|QQ')
6c: A/Q-Q/A-P/F-O/J-K1/D1-J'/O'-D1/K1 | A'/Q'-Q'/A'-K2/D2-O'/J'-D2/K2-J/O-F/P (APA'K2JK1,D1J'D2O',FO|Q,Q')
6d: A/Q-Q/A-P/F-O'/J'-K1/D1-J'/O'-D1/K1 | A'/Q'-Q'/A'-K2/D2-O/J-D2/K2-J/O-F/P (APA'K2JD2OFO'D1J'K1|Q,Q')

Solution 7: A/Q-Q/A-P/F-O/J-L1/I1-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-I2/L2-J/O-F/P
7a: A'/Q'-Q/A-P/F-O/J-L1/I1-I1/L1-B1/B1 | A/Q-Q'/A'-B2/B2-L2/I2-I2/L2-J/O-F/P (AP,A'B2L2JL1B1,FO,I1,I2|QQ')
7b: A/Q-Q/A-P/F-O/J-L1/I1-I1/L1-B1/B1 | A'/Q'-Q'/A'-B2/B2-L2/I2-I2/L2-J/O-F/P (APA'B2L2JL1B1,FO,I1,I2|Q,Q')

Solution 8: A/Q-Q/A-P/F-O/J-L1/I1-I1/L1-F/P | A/Q-Q/A-P/F-L2/I2-I2/L2-J/O-F/P
8a: A'/Q'-Q/A-P/F-O/J-L1/I1-I1/L1-F'/P' | A/Q-Q'/A'-P'/F'-L2/I2-I2/L2-J/O-F/P (AP,A'P',FO,F'L2JL1,I1,I2|QQ')
8b: A/Q-Q/A-P/F-O/J-L1/I1-I1/L1-F'/P' | A'/Q'-Q'/A'-P'/F'-L2/I2-I2/L2-J/O-F/P (APA'P',FO,F'L2JL1,I1,I2|Q,Q')

Solution 9: A/Q-Q/A-P/F-O/J-M/M-G1/C1-C1/G1 | A/Q-Q/A-G2/C2-C2/G2-M/M-J/O-F/P
9a: A'/Q'-Q/A-P/F-O/J-M'/M-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-M/M'-J/O-F/P (AP,A'G2MG1,JM',C1,C2,FO|QQ')
9b: A'/Q'-Q/A-P/F-O/J-M'/M'-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-M/M-J/O-F/P (AP,A'G2MJM'G1,C1,C2,FO|QQ')
9c: A/Q-Q/A-P/F-O/J-M'/M-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-M/M'-J/O-F/P (APA'G2MG1,JM',C1,C2,FO|Q,Q')
9d: A/Q-Q/A-P/F-O/J-M'/M'-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-M/M-J/O-F/P (APA'G2MJM'G1,C1,C2,FO|Q,Q')

Solution 10: A/Q-Q/A-P/F-O/J-M/M-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-M/M-J/O-F/P
10a: A'/Q'-Q/A-P/F-O/J-M'/M-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-M/M'-J/O-F/P (AP,A'B2H2MH1B1,FO,JM'|QQ')
10b: A'/Q'-Q/A-P/F-O/J-M'/M'-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-M/M-J/O-F/P (AP,A'B2H2MJM'H1B1,FO|QQ')
10c: A/Q-Q/A-P/F-O/J-M'/M-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-M/M'-J/O-F/P (APA'B2H2MH1B1,FO,JM'|Q,Q')
10d: A/Q-Q/A-P/F-O/J-M'/M'-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-M/M-J/O-F/P (APA'B2H2MJM'H1B1,FO|Q,Q')

Solution 11: A/Q-Q/A-P/F-O/J-M/M-H1/H1-F/P | A/Q-Q/A-P/F-H2/H2-M/M-J/O-F/P
11a: A'/Q'-Q/A-P/F-O/J-M'/M-H1/H1-F'/P' | A/Q-Q'/A'-P'/F'-H2/H2-M/M'-J/O-F/P (AP,A'P',FO,F'H2MH1,JM'|QQ')
11b: A'/Q'-Q/A-P/F-O/J-M'/M'-H1/H1-F'/P' | A/Q-Q'/A'-P'/F'-H2/H2-M/M-J/O-F/P (AP,A'P',FO,F'H2MJM'H1|QQ')
11c: A/Q-Q/A-P/F-O/J-M'/M-H1/H1-F'/P' | A'/Q'-Q'/A'-P'/F'-H2/H2-M/M'-J/O-F/P (APA'P',FO,F'H2MH1,JM'|Q,Q')
11d: A/Q-Q/A-P/F-O/J-M'/M'-H1/H1-F'/P' | A'/Q'-Q'/A'-P'/F'-H2/H2-M/M-J/O-F/P (APA'P',FO,F'H2MJM'H1|Q,Q')

Solution 12: A/Q-Q/A-P/F-O/J-M/M-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-M/M-J/O-F/P
12a: A'/Q'-Q/A-P/F-O'/J'-M'/M-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M/M'-J'/O'-F/P (AP,A'B2OB1,FO',JM,J'M'|QQ')
12b: A'/Q'-Q/A-P/F-O'/J'-M'/M'-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M/M-J'/O'-F/P (AP,A'B2OB1,FO',JMJ'M'|QQ')
12c: A'/Q'-Q/A-P/F-O'/J'-M'/M'-J'/O'-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M/M-J/O-F/P (AP,A'B2OFO'B1,JM,J'M'|QQ')
12d: A'/Q'-Q/A-P/F-O'/J'-M'/M-J'/O'-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M/M'-J/O-F/P (AP,A'B2OFO'B1,JMJ'M'|QQ')
12e: A/Q-Q/A-P/F-O'/J'-M'/M-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M/M'-J'/O'-F/P (APA'B2OB1,FO',JM,J'M'|Q,Q')
12f: A/Q-Q/A-P/F-O'/J'-M'/M'-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M/M-J'/O'-F/P (APA'B2OB1,FO',JMJ'M'|Q,Q')
12g: A/Q-Q/A-P/F-O'/J'-M'/M'-J'/O'-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M/M-J/O-F/P (APA'B2OFO'B1,JM,J'M'|Q,Q')
12h: A/Q-Q/A-P/F-O'/J'-M'/M-J'/O'-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M/M'-J/O-F/P (APA'B2OFO'B1,JMJ'M'|Q,Q')

Solution 13: A/Q-Q/A-P/F-O/J-M/M-J/O-F/P (AP,FO,JM|Q)

Solution 14: A/Q-Q/A-P/F-O/J-M/M-E2/N2-E1/N1 | A/Q-Q/A-N2/E2-N1/E1-M/M-J/O-F/P
14a: A'/Q'-Q/A-P/F-O/J-M'/M-E2/N2-E1/N1 | A/Q-Q'/A'-N2/E2-N1/E1-M/M'-J/O-F/P (AP,A'N2E1ME2N1,FO,JM'|QQ')
14b: A'/Q'-Q/A-P/F-O/J-M'/M'-E2/N2-E1/N1 | A/Q-Q'/A'-N2/E2-N1/E1-M/M-J/O-F/P (AP,A'N2E1MJM'E2N1,FO|QQ')
14c: A/Q-Q/A-P/F-O/J-M'/M-E2/N2-E1/N1 | A'/Q'-Q'/A'-N2/E2-N1/E1-M/M'-J/O-F/P (APA'N2E1ME2N1,FO,JM'|Q,Q')
14d: A/Q-Q/A-P/F-O/J-M'/M'-E2/N2-E1/N1 | A'/Q'-Q'/A'-N2/E2-N1/E1-M/M-J/O-F/P (APA'N2E1MJM'E2N1,FO|Q,Q')

Solution 15: A/Q-Q/A-P/F-O/J-I2/L2-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-L1/I1-J/O-F/P
15a: A'/Q'-Q/A-P/F-O/J-I2/L2-I1/L1-B1/B1 | A/Q-Q'/A'-B2/B2-L2/I2-L1/I1-J/O-F/P (AP,A'B2L2I1JI2L1B1,FO|QQ')
15b: A/Q-Q/A-P/F-O/J-I2/L2-I1/L1-B1/B1 | A'/Q'-Q'/A'-B2/B2-L2/I2-L1/I1-J/O-F/P (APA'B2L2I1JI2L1B1,FO|Q,Q')

Solution 16: A/Q-Q/A-P/F-O/J-I2/L2-I1/L1-F/P | A/Q-Q/A-P/F-L2/I2-L1/I1-J/O-F/P
16a: A'/Q'-Q/A-P/F-O/J-I2/L2-I1/L1-F'/P' | A/Q-Q'/A'-P'/F'-L2/I2-L1/I1-J/O-F/P (AP,A'P',FO,F'L2I1JI2L1|QQ')
16b: A/Q-Q/A-P/F-O/J-I2/L2-I1/L1-F'/P' | A'/Q'-Q'/A'-P'/F'-L2/I2-L1/I1-J/O-F/P (APA'P',FO,F'L2I1JI2L1|Q,Q')

Solution 17: A/Q-Q/A-P/F-O/J-D2/K2-H1/H1-D1/K1 | A/Q-Q/A-K2/D2-H2/H2-K1/D1-J/O-F/P
17a: A'/Q'-Q/A-P/F-O/J-D2/K2-H1/H1-D1/K1 | A/Q-Q'/A'-K2/D2-H2/H2-K1/D1-J/O-F/P (AP,A'K2H1D1JD2H2K1,FO|QQ')
17b: A/Q-Q/A-P/F-O/J-D2/K2-H1/H1-D1/K1 | A'/Q'-Q'/A'-K2/D2-H2/H2-K1/D1-J/O-F/P (APA'K2H1D1JD2H2K1,FO|Q,Q')

Solution 18: A/Q-Q/A-P/F-O/J-D2/K2-J/O-D1/K1 | A/Q-Q/A-K2/D2-O/J-K1/D1-J/O-F/P
18a: A'/Q'-Q/A-P/F-O'/J'-D2/K2-J/O-D1/K1 | A/Q-Q'/A'-K2/D2-O/J-K1/D1-J'/O'-F/P (AP,A'K2JK1,D1J'D2O,FO'|QQ')
18b: A'/Q'-Q/A-P/F-O/J-D2/K2-J/O-D1/K1 | A/Q-Q'/A'-K2/D2-O'/J'-K1/D1-J'/O'-F/P (AP,A'K2JD2O'FOD1J'K1|QQ')
18c: A/Q-Q/A-P/F-O'/J'-D2/K2-J/O-D1/K1 | A'/Q'-Q'/A'-K2/D2-O/J-K1/D1-J'/O'-F/P (APA'K2JK1,D1J'D2O,FO'|Q,Q')
18d: A/Q-Q/A-P/F-O/J-D2/K2-J/O-D1/K1 | A'/Q'-Q'/A'-K2/D2-O'/J'-K1/D1-J'/O'-F/P (APA'K2JD2O'FOD1J'K1|Q,Q')

Solution 19: A/Q-Q/A-P/F-L2/I2-L1/I1-G1/C1-C1/G1 | A/Q-Q/A-G2/C2-C2/G2-I2/L2-I1/L1-F/P
19a: A'/Q'-Q/A-P/F-L2/I2-L1/I1-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-I2/L2-I1/L1-F/P (AP,A'G2I2L1FL2I1G1,C1,C2|QQ')
19b: A/Q-Q/A-P/F-L2/I2-L1/I1-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-I2/L2-I1/L1-F/P (APA'G2I2L1FL2I1G1,C1,C2|Q,Q')

Solution 20: A/Q-Q/A-P/F-L2/I2-L1/I1-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-I2/L2-I1/L1-F/P
20a: A'/Q'-Q/A-P/F-L2/I2-L1/I1-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-I2/L2-I1/L1-F/P (AP,A'B2H2I2L1FL2I1H1B1|QQ')
20a: A/Q-Q/A-P/F-L2/I2-L1/I1-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-I2/L2-I1/L1-F/P (APA'B2H2I2L1FL2I1H1B1|Q,Q')

Solution 21: A/Q-Q/A-P/F-L2/I2-L1/I1-H1/H1-F/P | A/Q-Q/A-P/F-H2/H2-I2/L2-I1/L1-F/P
21a: A'/Q'-Q/A-P/F-L2/I2-L1/I1-H1/H1-F'/P' | A/Q-Q'/A'-P'/F'-H2/H2-I2/L2-I1/L1-F/P (AP,A'P',FL2I1H1F'H2I2L1|QQ')
21b: A/Q-Q/A-P/F-L2/I2-L1/I1-H1/H1-F'/P' | A'/Q'-Q'/A'-P'/F'-H2/H2-I2/L2-I1/L1-F/P (APA'P',FL2I1H1F'H2I2L1|Q,Q')

Solution 22: A/Q-Q/A-P/F-L2/I2-L1/I1-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-I2/L2-I1/L1-F/P
22a: A'/Q'-Q/A-P/F-L2/I2-L1/I1-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-I2/L2-I1/L1-F/P (AP,A'B2OB1,FL2I1JI2L1|QQ')
22b: A/Q-Q/A-P/F-L2/I2-L1/I1-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-I2/L2-I1/L1-F/P (APA'B2OB1,FL2I1JI2L1|Q,Q')

Solution 23: A/Q-Q/A-P/F-L2/I2-L1/I1-E2/N2-E1/N1 | A/Q-Q/A-N2/E2-N1/E1-I2/L2-I1/L1-F/P
23a: A'/Q'-Q/A-P/F-L2/I2-L1/I1-E2/N2-E1/N1 | A/Q-Q'/A'-N2/E2-N1/E1-I2/L2-I1/L1-F/P (AP,A'N2E1I2L1FL2I1E2N1|QQ')
23b: A/Q-Q/A-P/F-L2/I2-L1/I1-E2/N2-E1/N1 | A'/Q'-Q'/A'-N2/E2-N1/E1-I2/L2-I1/L1-F/P (APA'N2E1I2L1FL2I1E2N1|Q,Q')

Solution 24: A/Q-Q/A-P/F-L2/I2-I2/L2-G1/C1-C1/G1 | A/Q-Q/A-G2/C2-C2/G2-L1/I1-I1/L1-F/P
24a: A'/Q'-Q/A-P/F-L2/I2-I2/L2-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-L1/I1-I1/L1-F/P (AP,A'G2L1FL2G1,C1,I1,I2,C2|QQ')
24b: A/Q-Q/A-P/F-L2/I2-I2/L2-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-L1/I1-I1/L1-F/P (APA'G2L1FL2G1,C1,I1,I2,C2|Q,Q')

Solution 25: A/Q-Q/A-P/F-L2/I2-I2/L2-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-L1/I1-I1/L1-F/P
25a: A'/Q'-Q/A-P/F-L2/I2-I2/L2-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-L1/I1-I1/L1-F/P (AP,A'B2H2L1FL2H1B1,I1,I2|QQ')
25b: A/Q-Q/A-P/F-L2/I2-I2/L2-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-L1/I1-I1/L1-F/P (APA'B2H2L1FL2H1B1,I1,I2|Q,Q')

Solution 26: A/Q-Q/A-P/F-L2/I2-I2/L2-H1/H1-F/P | A/Q-Q/A-P/F-H2/H2-L1/I1-I1/L1-F/P
26a: A'/Q'-Q/A-P/F-L2/I2-I2/L2-H1/H1-F'/P' | A/Q-Q'/A'-P'/F'-H2/H2-L1/I1-I1/L1-F/P (AP,A'P',FL2H1F'H2L1,I1,I2|QQ')
26b: A/Q-Q/A-P/F-L2/I2-I2/L2-H1/H1-F'/P' | A'/Q'-Q'/A'-P'/F'-H2/H2-L1/I1-I1/L1-F/P (APA'P',FL2H1F'H2L1,I1,I2|Q,Q')

Solution 27: A/Q-Q/A-P/F-L2/I2-I2/L2-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-L1/I1-I1/L1-F/P
27a: A'/Q'-Q/A-P/F-L2/I2-I2/L2-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-L1/I1-I1/L1-F/P (AP,A'B2OB1,FL2JL1,I1,I2|QQ')
27b: A/Q-Q/A-P/F-L2/I2-I2/L2-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-L1/I1-I1/L1-F/P (APA'B2OB1,FL2JL1,I1,I2|Q,Q')

Solution 28: A/Q-Q/A-P/F-L2/I2-I2/L2-E2/N2-E1/N1 | A/Q-Q/A-N2/E2-N1/E1-L1/I1-I1/L1-F/P
28a: A'/Q'-Q/A-P/F-L2/I2-I2/L2-E2/N2-E1/N1 | A/Q-Q'/A'-N2/E2-N1/E1-L1/I1-I1/L1-F/P (AP,A'N2E1L1FL2E2N1,I1,I2|QQ')
28b: A/Q-Q/A-P/F-L2/I2-I2/L2-E2/N2-E1/N1 | A'/Q'-Q'/A'-N2/E2-N1/E1-L1/I1-I1/L1-F/P (APA'N2E1L1FL2E2N1,I1,I2|Q,Q')

Solution 29: A/Q-Q/A-P/F-H2/H2-K1/D1-H1/H1-D1/K1 | A/Q-Q/A-K2/D2-H2/H2-D2/K2-H1/H1-F/P
29a: A'/Q'-Q/A-P/F-H2/H2-K1/D1-H1'/H1'-D1/K1 | A/Q-Q'/A'-K2/D2-H2'/H2'-D2/K2-H1/H1-F/P (AP,A'K2H1FH2K1,D1H1',D2H2'|QQ')
29b: A'/Q'-Q/A-P/F-H2/H2'-K1/D1-H1'/H1-D1/K1 | A/Q-Q'/A'-K2/D2-H2'/H2-D2/K2-H1/H1'-F/P (AP,A'K2H1D1H1'FH2D2H2'K1|QQ')
29c: A/Q-Q/A-P/F-H2/H2-K1/D1-H1'/H1'-D1/K1 | A'/Q'-Q'/A'-K2/D2-H2'/H2'-D2/K2-H1/H1-F/P (APA'K2H1FH2K1,D1H1',D2H2'|Q,Q')
29d: A/Q-Q/A-P/F-H2/H2'-K1/D1-H1'/H1-D1/K1 | A'/Q'-Q'/A'-K2/D2-H2'/H2-D2/K2-H1/H1'-F/P (APA'K2H1D1H1'FH2D2H2'K1|Q,Q')

Solution 30: A/Q-Q/A-P/F-H2/H2-K1/D1-J/O-D1/K1 | A/Q-Q/A-K2/D2-O/J-D2/K2-H1/H1-F/P
30a: A'/Q'-Q/A-P/F-H2/H2-K1/D1-J/O-D1/K1 | A/Q-Q'/A'-K2/D2-O/J-D2/K2-H1/H1-F/P (AP,A'K2H1FH2K1,D1JD2O|QQ')
30b: A/Q-Q/A-P/F-H2/H2-K1/D1-J/O-D1/K1 | A'/Q'-Q'/A'-K2/D2-O/J-D2/K2-H1/H1-F/P (APA'K2H1FH2K1,D1JD2O|Q,Q')

Solution 31: A/Q-Q/A-P/F-H2/H2-L1/I1-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-I2/L2-H1/H1-F/P
31a: A'/Q'-Q/A-P/F-H2/H2-L1/I1-I1/L1-B1/B1 | A/Q-Q'/A'-B2/B2-L2/I2-I2/L2-H1/H1-F/P (AP,A'B2L2H1FH2L1B1,I1,I2|QQ')
31b: A/Q-Q/A-P/F-H2/H2-L1/I1-I1/L1-B1/B1 | A'/Q'-Q'/A'-B2/B2-L2/I2-I2/L2-H1/H1-F/P (APA'B2L2H1FH2L1B1,I1,I2|Q,Q')

Solution 32: A/Q-Q/A-P/F-H2/H2-M/M-G1/C1-C1/G1 | A/Q-Q/A-G2/C2-C2/G2-M/M-H1/H1-F/P
32a: A'/Q'-Q/A-P/F-H2/H2-M'/M-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-M/M'-H1/H1-F/P (AP,A'G2MG1,C1,C2,FH2M'H1|QQ')
32b: A'/Q'-Q/A-P/F-H2/H2-M'/M'-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-M/M-H1/H1-F/P (AP,A'G2MH1FH2M'G1,C1,C2|QQ')
32c: A/Q-Q/A-P/F-H2/H2-M'/M-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-M/M'-H1/H1-F/P (APA'G2MG1,C1,C2,FH2M'H1|Q,Q')
32d: A/Q-Q/A-P/F-H2/H2-M'/M'-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-M/M-H1/H1-F/P (APA'G2MH1FH2M'G1,C1,C2|Q,Q')

Solution 33: A/Q-Q/A-P/F-H2/H2-M/M-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-M/M-H1/H1-F/P
33a: A'/Q'-Q/A-P/F-H2'/H2'-M'/M'-H1'/H1'-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-M/M-H1/H1-F/P (AP,A'B2H2MH1FH2'M'H1'B1|QQ')
33b: A'/Q'-Q/A-P/F-H2'/H2'-M'/M-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-M/M'-H1'/H1'-F/P (AP,A'B2H2MH1B1,FH2'M'H1'|QQ')
33c: A'/Q'-Q/A-P/F-H2'/H2-M/M-H1/H1'-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2'-M'/M'-H1'/H1-F/P (AP,A'B2H2MH1FH2'M'H1'B1|QQ')
33d: A'/Q'-Q/A-P/F-H2'/H2-M/M'-H1'/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2'-M'/M-H1/H1'-F/P (AP,A'B2H2MH1B1,FH2'M'H1'|QQ')
33e: A/Q-Q/A-P/F-H2'/H2'-M'/M'-H1'/H1'-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-M/M-H1/H1-F/P (APA'B2H2MH1FH2'M'H1'B1|Q,Q')
33f: A/Q-Q/A-P/F-H2'/H2'-M'/M-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-M/M'-H1'/H1'-F/P (APA'B2H2MH1B1,FH2'M'H1'|Q,Q')
33g: A/Q-Q/A-P/F-H2'/H2-M/M-H1/H1'-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2'-M'/M'-H1'/H1-F/P (APA'B2H2MH1FH2'M'H1'B1|Q,Q')
33h: A/Q-Q/A-P/F-H2'/H2-M/M'-H1'/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2'-M'/M-H1/H1'-F/P (APA'B2H2MH1B1,FH2'M'H1'|Q,Q')

Solution 34: A/Q-Q/A-P/F-H2/H2-M/M-H1/H1-F/P (AP,FH2MH1|Q)

Solution 35: A/Q-Q/A-P/F-H2/H2-M/M-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-M/M-H1/H1-F/P
35a: A'/Q'-Q/A-P/F-H2/H2-M/M'-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M'/M-H1/H1-F/P (AP,A'B2OB1,FH2MH1,JM'|QQ')
35b: A'/Q'-Q/A-P/F-H2/H2-M/M-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M'/M'-H1/H1-F/P (AP,A'B2OB1,FH2MJM'H1|QQ')
35c: A/Q-Q/A-P/F-H2/H2-M/M'-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M'/M-H1/H1-F/P (APA'B2OB1,FH2MH1,JM'|Q,Q')
35d: A/Q-Q/A-P/F-H2/H2-M/M-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M'/M'-H1/H1-F/P (APA'B2OB1,FH2MJM'H1|Q,Q')

Solution 36: A/Q-Q/A-P/F-H2/H2-M/M-E2/N2-E1/N1 | A/Q-Q/A-N2/E2-N1/E1-M/M-H1/H1-F/P
36a: A'/Q'-Q/A-P/F-H2/H2-M'/M-E2/N2-E1/N1 | A/Q-Q'/A'-N2/E2-N1/E1-M/M'-H1/H1-F/P (AP,A'N2E1ME2N1,FH2M'H1|QQ')
36b: A'/Q'-Q/A-P/F-H2/H2-M'/M'-E2/N2-E1/N1 | A/Q-Q'/A'-N2/E2-N1/E1-M/M-H1/H1-F/P (AP,A'N2E1MH1FH2M'E2N1|QQ')
36c: A/Q-Q/A-P/F-H2/H2-M'/M-E2/N2-E1/N1 | A'/Q'-Q'/A'-N2/E2-N1/E1-M/M'-H1/H1-F/P (APA'N2E1ME2N1,FH2M'H1|Q,Q')
36d: A/Q-Q/A-P/F-H2/H2-M'/M'-E2/N2-E1/N1 | A'/Q'-Q'/A'-N2/E2-N1/E1-M/M-H1/H1-F/P (APA'N2E1MH1FH2M'E2N1|Q,Q')

Solution 37: A/Q-Q/A-P/F-H2/H2-I2/L2-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-L1/I1-H1/H1-F/P
37a: A'/Q'-Q/A-P/F-H2/H2-I2/L2-I1/L1-B1/B1 | A/Q-Q'/A'-B2/B2-L2/I2-L1/I1-H1/H1-F/P (AP,A'B2L2I1H1FH2I2L1B1|QQ')
37b: A/Q-Q/A-P/F-H2/H2-I2/L2-I1/L1-B1/B1 | A'/Q'-Q'/A'-B2/B2-L2/I2-L1/I1-H1/H1-F/P (APA'B2L2I1H1FH2I2L1B1|Q,Q')

Solution 38: A/Q-Q/A-P/F-H2/H2-D2/K2-H1/H1-D1/K1 | A/Q-Q/A-K2/D2-H2/H2-K1/D1-H1/H1-F/P
38a: A'/Q'-Q/A-P/F-H2/H2-D2/K2-H1/H1-D1/K1 | A/Q-Q'/A'-K2/D2-H2'/H2'-K1/D1-H1'/H1'-F/P (AP,A'K2H1D1H1'FH2D2H2'K1|QQ')
38b: A'/Q'-Q/A-P/F-H2/H2'-D2/K2-H1/H1'-D1/K1 | A/Q-Q'/A'-K2/D2-H2'/H2-K1/D1-H1'/H1-F/P (AP,A'K2H1FH2K1,D1H1',D2H2'|QQ')
38c: A/Q-Q/A-P/F-H2/H2-D2/K2-H1/H1-D1/K1 | A'/Q'-Q'/A'-K2/D2-H2'/H2'-K1/D1-H1'/H1'-F/P (APA'K2H1D1H1'FH2D2H2'K1|Q,Q')
38d: A/Q-Q/A-P/F-H2/H2'-D2/K2-H1/H1'-D1/K1 | A'/Q'-Q'/A'-K2/D2-H2'/H2-K1/D1-H1'/H1-F/P (APA'K2H1FH2K1,D1H1',D2H2'|Q,Q')

Solution 39: A/Q-Q/A-P/F-H2/H2-D2/K2-J/O-D1/K1 | A/Q-Q/A-K2/D2-O/J-K1/D1-H1/H1-F/P
39a: A'/Q'-Q/A-P/F-H2/H2-D2/K2-J/O-D1/K1 | A/Q-Q'/A'-K2/D2-O/J-K1/D1-H1/H1-F/P (AP,A'K2JK1,D1H1FH2D2O|QQ')
39b: A/Q-Q/A-P/F-H2/H2-D2/K2-J/O-D1/K1 | A'/Q'-Q'/A'-K2/D2-O/J-K1/D1-H1/H1-F/P (APA'K2JK1,D1H1FH2D2O|Q,Q')

Solution 40: A/Q-Q/A-P/F-C2/G2-L1/I1-I1/L1-C1/G1 | A/Q-Q/A-G2/C2-L2/I2-I2/L2-G1/C1-F/P
40a: A'/Q'-Q/A-P/F-C2/G2-L1/I1-I1/L1-C1/G1 | A/Q-Q'/A'-G2/C2-L2/I2-I2/L2-G1/C1-F/P (AP,A'G2L1C1FC2L2G1,I1,I2|QQ')
40b: A/Q-Q/A-P/F-C2/G2-L1/I1-I1/L1-C1/G1 | A'/Q'-Q'/A'-G2/C2-L2/I2-I2/L2-G1/C1-F/P (APA'G2L1C1FC2L2G1,I1,I2|Q,Q')

Solution 41: A/Q-Q/A-P/F-C2/G2-M/M-H1/H1-C1/G1 | A/Q-Q/A-G2/C2-H2/H2-M/M-G1/C1-F/P
41a: A'/Q'-Q/A-P/F-C2/G2-M/M'-H1/H1-C1/G1 | A/Q-Q'/A'-G2/C2-H2/H2-M'/M-G1/C1-F/P (AP,A'G2MG1,C1FC2H2M'H1|QQ')
41b: A'/Q'-Q/A-P/F-C2/G2-M/M-H1/H1-C1/G1 | A/Q-Q'/A'-G2/C2-H2/H2-M'/M'-G1/C1-F/P (AP,A'G2MH1C1FC2H2M'G1|QQ')
41c: A/Q-Q/A-P/F-C2/G2-M/M'-H1/H1-C1/G1 | A'/Q'-Q'/A'-G2/C2-H2/H2-M'/M-G1/C1-F/P (APA'G2MG1,C1FC2H2M'H1|Q,Q')
41d: A/Q-Q/A-P/F-C2/G2-M/M-H1/H1-C1/G1 | A'/Q'-Q'/A'-G2/C2-H2/H2-M'/M'-G1/C1-F/P (APA'G2MH1C1FC2H2M'G1|Q,Q')

Solution 42: A/Q-Q/A-P/F-C2/G2-M/M-J/O-C1/G1 | A/Q-Q/A-G2/C2-O/J-M/M-G1/C1-F/P
42a: A'/Q'-Q/A-P/F-C2/G2-M/M'-J/O-C1/G1 | A/Q-Q'/A'-G2/C2-O/J-M'/M-G1/C1-F/P (AP,A'G2MG1,C1FC2O,JM'|QQ')
42b: A'/Q'-Q/A-P/F-C2/G2-M/M-J/O-C1/G1 | A/Q-Q'/A'-G2/C2-O/J-M'/M'-G1/C1-F/P (AP,A'G2MJM'G1,C1FC2O|QQ')
42c: A/Q-Q/A-P/F-C2/G2-M/M'-J/O-C1/G1 | A'/Q'-Q'/A'-G2/C2-O/J-M'/M-G1/C1-F/P (APA'G2MG1,C1FC2O,JM'|Q,Q')
42d: A/Q-Q/A-P/F-C2/G2-M/M-J/O-C1/G1 | A'/Q'-Q'/A'-G2/C2-O/J-M'/M'-G1/C1-F/P (APA'G2MJM'G1,C1FC2O|Q,Q')

Solution 43: A/Q-Q/A-P/F-C2/G2-I2/L2-I1/L1-C1/G1 | A/Q-Q/A-G2/C2-L2/I2-L1/I1-G1/C1-F/P
43a: A'/Q'-Q/A-P/F-C2/G2-I2/L2-I1/L1-C1/G1 | A/Q-Q'/A'-G2/C2-L2/I2-L1/I1-G1/C1-F/P (AP,A'G2I2L1C1FC2L2I1G1|QQ')
43b: A/Q-Q/A-P/F-C2/G2-I2/L2-I1/L1-C1/G1 | A'/Q'-Q'/A'-G2/C2-L2/I2-L1/I1-G1/C1-F/P (APA'G2I2L1C1FC2L2I1G1|Q,Q')

Solution 44: A/Q-Q/A-N2/E2-N1/E1-K1/D1-H1/H1-D1/K1 | A/Q-Q/A-K2/D2-H2/H2-D2/K2-E2/N2-E1/N1
44a: A'/Q'-Q/A-N2/E2-N1/E1-K1/D1-H1/H1-D1/K1 | A/Q-Q'/A'-K2/D2-H2/H2-D2/K2-E2/N2-E1/N1 (AN2E1K1A'K2E2N1,D1H1,D2H2|QQ')
44b: A/Q-Q/A-N2/E2-N1/E1-K1/D1-H1/H1-D1/K1 | A'/Q'-Q'/A'-K2/D2-H2/H2-D2/K2-E2/N2-E1/N1 (AN2E1K1,A'K2E2N1,D1H1,D2H2|Q,Q')

Solution 45: A/Q-Q/A-N2/E2-N1/E1-K1/D1-J/O-D1/K1 | A/Q-Q/A-K2/D2-O/J-D2/K2-E2/N2-E1/N1
45a: A'/Q'-Q/A-N2/E2-N1/E1-K1/D1-J/O-D1/K1 | A/Q-Q'/A'-K2/D2-O/J-D2/K2-E2/N2-E1/N1 (AN2E1K1A'K2E2N1,D1JD2O|QQ')
45b: A/Q-Q/A-N2/E2-N1/E1-K1/D1-J/O-D1/K1 | A'/Q'-Q'/A'-K2/D2-O/J-D2/K2-E2/N2-E1/N1 (AN2E1K1,A'K2E2N1,D1JD2O|Q,Q')

Solution 46: A/Q-Q/A-N2/E2-N1/E1-L1/I1-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-I2/L2-E2/N2-E1/N1
46a: A'/Q'-Q/A-N2/E2-N1/E1-L1/I1-I1/L1-B1/B1 | A/Q-Q'/A'-B2/B2-L2/I2-I2/L2-E2/N2-E1/N1 (AN2E1L1B1A'B2L2E2N1,I1,I2|QQ')
46b: A/Q-Q/A-N2/E2-N1/E1-L1/I1-I1/L1-B1/B1 | A'/Q'-Q'/A'-B2/B2-L2/I2-I2/L2-E2/N2-E1/N1 (AN2E1L1B1,A'B2L2E2N1,I1,I2|Q,Q')

Solution 47: A/Q-Q/A-N2/E2-N1/E1-M/M-G1/C1-C1/G1 | A/Q-Q/A-G2/C2-C2/G2-M/M-E2/N2-E1/N1
47a: A'/Q'-Q/A-N2/E2-N1/E1-M/M'-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-M'/M-E2/N2-E1/N1 (AN2E1ME2N1,A'G2M'G1,C1,C2|QQ')
47b: A'/Q'-Q/A-N2/E2-N1/E1-M/M-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-M'/M'-E2/N2-E1/N1 (AN2E1MG1A'G2M'E2N1,C1,C2|QQ')
47c: A/Q-Q/A-N2/E2-N1/E1-M/M'-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-M'/M-E2/N2-E1/N1 (AN2E1ME2N1A'G2M'G1,C1,C2|Q,Q')
47d: A/Q-Q/A-N2/E2-N1/E1-M/M-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-M'/M'-E2/N2-E1/N1 (AN2E1MG1,A'G2M'E2N1,C1,C2|Q,Q')

Solution 48: A/Q-Q/A-N2/E2-N1/E1-M/M-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-M/M-E2/N2-E1/N1
48a: A'/Q'-Q/A-N2/E2-N1/E1-M/M'-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-M'/M-E2/N2-E1/N1 (AN2E1ME2N1,A'B2H2M'H1B1|QQ')
48b: A'/Q'-Q/A-N2/E2-N1/E1-M/M-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-M'/M'-E2/N2-E1/N1 (AN2E1MH1B1A'B2H2M'E2N1|QQ')
48c: A/Q-Q/A-N2/E2-N1/E1-M/M'-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-M'/M-E2/N2-E1/N1 (AN2E1ME2N1A'B2H2M'H1B1|Q,Q')
48d: A/Q-Q/A-N2/E2-N1/E1-M/M-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-M'/M'-E2/N2-E1/N1 (AN2E1MH1B1,A'B2H2M'E2N1|Q,Q')

Solution 49: A/Q-Q/A-N2/E2-N1/E1-M/M-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-M/M-E2/N2-E1/N1
49a: A'/Q'-Q/A-N2/E2-N1/E1-M/M'-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M'/M-E2/N2-E1/N1 (AN2E1ME2N1,A'B2OB1,JM'|QQ')
49b: A'/Q'-Q/A-N2/E2-N1/E1-M/M-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M'/M'-E2/N2-E1/N1 (AN2E1MJM'E2N1,A'B2OB1|QQ')
49c: A/Q-Q/A-N2/E2-N1/E1-M/M'-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M'/M-E2/N2-E1/N1 (AN2E1ME2N1A'B2OB1,JM'|Q,Q')
49d: A/Q-Q/A-N2/E2-N1/E1-M/M-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M'/M'-E2/N2-E1/N1 (AN2E1MJM'E2N1A'B2OB1|Q,Q')

Solution 50: A/Q-Q/A-N2/E2-N1/E1-M/M-E2/N2-E1/N1 (AN2E1ME2N1|Q)

Solution 51: A/Q-Q/A-N2/E2-N1/E1-I2/L2-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-L1/I1-E2/N2-E1/N1
51a: A'/Q'-Q/A-N2/E2-N1/E1-I2/L2-I1/L1-B1/B1 | A/Q-Q'/A'-B2/B2-L2/I2-L1/I1-E2/N2-E1/N1 (AN2E1I2L1B1A'B2L2I1E2N1|QQ')
51b: A/Q-Q/A-N2/E2-N1/E1-I2/L2-I1/L1-B1/B1 | A'/Q'-Q'/A'-B2/B2-L2/I2-L1/I1-E2/N2-E1/N1 (AN2E1I2L1B1,A'B2L2I1E2N1|Q,Q')

Solution 52: A/Q-Q/A-N2/E2-N1/E1-D2/K2-H1/H1-D1/K1 | A/Q-Q/A-K2/D2-H2/H2-K1/D1-E2/N2-E1/N1
52a: A'/Q'-Q/A-N2/E2-N1/E1-D2/K2-H1/H1-D1/K1 | A/Q-Q'/A'-K2/D2-H2/H2-K1/D1-E2/N2-E1/N1 (AN2E1D2H2K1A'K2H1D1E2N1|QQ')
52b: A/Q-Q/A-N2/E2-N1/E1-D2/K2-H1/H1-D1/K1 | A'/Q'-Q'/A'-K2/D2-H2/H2-K1/D1-E2/N2-E1/N1 (AN2E1D2H2K1,A'K2H1D1E2N1|Q,Q')

Solution 53: A/Q-Q/A-N2/E2-N1/E1-D2/K2-J/O-D1/K1 | A/Q-Q/A-K2/D2-O/J-K1/D1-E2/N2-E1/N1
53a: A'/Q'-Q/A-N2/E2-N1/E1-D2/K2-J/O-D1/K1 | A/Q-Q'/A'-K2/D2-O/J-K1/D1-E2/N2-E1/N1 (AN2E1D2OD1E2N1,A'K2JK1|QQ')
53b: A/Q-Q/A-N2/E2-N1/E1-D2/K2-J/O-D1/K1 | A'/Q'-Q'/A'-K2/D2-O/J-K1/D1-E2/N2-E1/N1 (AN2E1D2OD1E2N1A'K2JK1|Q,Q')

Solution 54: A/Q-Q/A-N2/E2-O/J-K1/D1-E2/N2-D1/K1 | A/Q-Q/A-K2/D2-N1/E1-D2/K2-J/O-E1/N1
54a: A'/Q'-Q/A-N2/E2-O/J-K1/D1-E2/N2-D1/K1 | A/Q-Q'/A'-K2/D2-N1/E1-D2/K2-J/O-E1/N1 (AN2D1E2OE1D2N1,A'K2JK1|QQ')
54b: A/Q-Q/A-N2/E2-O/J-K1/D1-E2/N2-D1/K1 | A'/Q'-Q'/A'-K2/D2-N1/E1-D2/K2-J/O-E1/N1 (AN2D1E2OE1D2N1A'K2JK1|Q,Q')

Solution 55: A/Q-Q/A-N2/E2-O/J-M/M-E2/N2-B1/B1 | A/Q-Q/A-B2/B2-N1/E1-M/M-J/O-E1/N1
55a: A'/Q'-Q/A-N2/E2-O/J-M'/M-E2/N2-B1/B1 | A/Q-Q'/A'-B2/B2-N1/E1-M/M'-J/O-E1/N1 (AN2B1A'B2N1,E1ME2O,JM'|QQ')
55b: A'/Q'-Q/A-N2/E2-O/J-M'/M'-E2/N2-B1/B1 | A/Q-Q'/A'-B2/B2-N1/E1-M/M-J/O-E1/N1 (AN2B1A'B2N1,E1MJM'E2O|QQ')
55c: A/Q-Q/A-N2/E2-O/J-M'/M-E2/N2-B1/B1 | A'/Q'-Q'/A'-B2/B2-N1/E1-M/M'-J/O-E1/N1 (AN2B1,A'B2N1,E1ME2O,JM'|Q,Q')
55d: A/Q-Q/A-N2/E2-O/J-M'/M'-E2/N2-B1/B1 | A'/Q'-Q'/A'-B2/B2-N1/E1-M/M-J/O-E1/N1 (AN2B1,A'B2N1,E1MJM'E2O|Q,Q')

Solution 56: A/Q-Q/A-N2/E2-O/J-D2/K2-E2/N2-D1/K1 | A/Q-Q/A-K2/D2-N1/E1-K1/D1-J/O-E1/N1
56a: A'/Q'-Q/A-N2/E2-O/J-D2/K2-E2/N2-D1/K1 | A/Q-Q'/A'-K2/D2-N1/E1-K1/D1-J/O-E1/N1 (AN2D1JD2N1,A'K2E2OE1K1|QQ')
56b: A/Q-Q/A-N2/E2-O/J-D2/K2-E2/N2-D1/K1 | A'/Q'-Q'/A'-K2/D2-N1/E1-K1/D1-J/O-E1/N1 (AN2D1JD2N1A'K2E2OE1K1|Q,Q')

Solution 57: A/Q-Q/A-N2/E2-L2/I2-L1/I1-E2/N2-B1/B1 | A/Q-Q/A-B2/B2-N1/E1-I2/L2-I1/L1-E1/N1
57a: A'/Q'-Q/A-N2/E2-L2/I2-L1/I1-E2/N2-B1/B1 | A/Q-Q'/A'-B2/B2-N1/E1-I2/L2-I1/L1-E1/N1 (AN2B1A'B2N1,E1I2L1,I1E2L2|QQ')
57b: A/Q-Q/A-N2/E2-L2/I2-L1/I1-E2/N2-B1/B1 | A'/Q'-Q'/A'-B2/B2-N1/E1-I2/L2-I1/L1-E1/N1 (AN2B1,A'B2N1,E1I2L1,I1E2L2|Q,Q')

Solution 58: A/Q-Q/A-N2/E2-L2/I2-I2/L2-E2/N2-B1/B1 | A/Q-Q/A-B2/B2-N1/E1-L1/I1-I1/L1-E1/N1
58a: A'/Q'-Q/A-N2/E2-L2/I2-I2/L2-E2/N2-B1/B1 | A/Q-Q'/A'-B2/B2-N1/E1-L1/I1-I1/L1-E1/N1 (AN2B1A'B2N1,E1L1,I1,E2L2,I2|QQ')
58b (chiral): A/Q-Q/A-N2/E2-L2/I2-I2/L2-E2/N2-B1/B1 | A'/Q'-Q'/A'-B2/B2-N1/E1-L1/I1-I1/L1-E1/N1 (AN2B1,E2L2,I2|Q)/(A'B2N1,E1L1,I1|Q')

Solution 59: A/Q-Q/A-N2/E2-H2/H2-K1/D1-E2/N2-D1/K1 | A/Q-Q/A-K2/D2-N1/E1-D2/K2-H1/H1-E1/N1
59a: A'/Q'-Q/A-N2/E2-H2/H2-K1/D1-E2/N2-D1/K1 | A/Q-Q'/A'-K2/D2-N1/E1-D2/K2-H1/H1-E1/N1 (AN2D1E2H2K1A'K2H1E1D2N1|QQ')
59b: A/Q-Q/A-N2/E2-H2/H2-K1/D1-E2/N2-D1/K1 | A'/Q'-Q'/A'-K2/D2-N1/E1-D2/K2-H1/H1-E1/N1 (AN2D1E2H2K1,A'K2H1E1D2N1|Q,Q')

Solution 60: A/Q-Q/A-N2/E2-H2/H2-M/M-E2/N2-B1/B1 | A/Q-Q/A-B2/B2-N1/E1-M/M-H1/H1-E1/N1
60a: A'/Q'-Q/A-N2/E2-H2/H2-M'/M-E2/N2-B1/B1 | A/Q-Q'/A'-B2/B2-N1/E1-M/M'-H1/H1-E1/N1 (AN2B1A'B2N1,E1ME2H2M'H1|QQ')
60b: A'/Q'-Q/A-N2/E2-H2/H2-M'/M'-E2/N2-B1/B1 | A/Q-Q'/A'-B2/B2-N1/E1-M/M-H1/H1-E1/N1 (AN2B1A'B2N1,E1MH1,E2H2M'|QQ')
60c: A/Q-Q/A-N2/E2-H2/H2-M'/M-E2/N2-B1/B1 | A'/Q'-Q'/A'-B2/B2-N1/E1-M/M'-H1/H1-E1/N1 (AN2B1,A'B2N1,E1ME2H2M'H1|Q,Q')
60d (chiral): A/Q-Q/A-N2/E2-H2/H2-M'/M'-E2/N2-B1/B1 | A'/Q'-Q'/A'-B2/B2-N1/E1-M/M-H1/H1-E1/N1 (AN2B1,E2H2M'|Q)/(A'B2N1,E1MH1|Q')

Solution 61: A/Q-Q/A-N2/E2-H2/H2-D2/K2-E2/N2-D1/K1 | A/Q-Q/A-K2/D2-N1/E1-K1/D1-H1/H1-E1/N1
61a: A'/Q'-Q/A-N2/E2-H2/H2-D2/K2-E2/N2-D1/K1 | A/Q-Q'/A'-K2/D2-N1/E1-K1/D1-H1/H1-E1/N1 (AN2D1H1E1K1A'K2E2H2D2N1|QQ')
61b: A/Q-Q/A-N2/E2-H2/H2-D2/K2-E2/N2-D1/K1 | A'/Q'-Q'/A'-K2/D2-N1/E1-K1/D1-H1/H1-E1/N1 (AN2D1H1E1K1,A'K2E2H2D2N1|Q,Q')

Solution 62: A/Q-Q/A-N2/E2-C2/G2-M/M-E2/N2-C1/G1 | A/Q-Q/A-G2/C2-N1/E1-M/M-G1/C1-E1/N1
62a: A'/Q'-Q/A-N2/E2-C2/G2-M'/M-E2/N2-C1/G1 | A/Q-Q'/A'-G2/C2-N1/E1-M/M'-G1/C1-E1/N1 (AN2C1E1ME2C2N1,A'G2M'G1|QQ')
62b: A'/Q'-Q/A-N2/E2-C2/G2-M'/M'-E2/N2-C1/G1 | A/Q-Q'/A'-G2/C2-N1/E1-M/M-G1/C1-E1/N1 (AN2C1E1MG1A'G2M'E2C2N1|QQ')
62c: A/Q-Q/A-N2/E2-C2/G2-M'/M-E2/N2-C1/G1 | A'/Q'-Q'/A'-G2/C2-N1/E1-M/M'-G1/C1-E1/N1 (AN2C1E1ME2C2N1A'G2M'G1|Q,Q')
62d: A/Q-Q/A-N2/E2-C2/G2-M'/M'-E2/N2-C1/G1 | A'/Q'-Q'/A'-G2/C2-N1/E1-M/M-G1/C1-E1/N1 (AN2C1E1MG1,A'G2M'E2C2N1|Q,Q')

Solution 63: A/Q-Q/A-K2/D2-O/J-K1/D1-G1/C1-C1/G1 | A/Q-Q/A-G2/C2-C2/G2-D2/K2-J/O-D1/K1
63a: A'/Q'-Q/A-K2/D2-O/J-K1/D1-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-D2/K2-J/O-D1/K1 (AK2JK1,A'G2D2OD1G1,C1,C2,QQ')
63b: A/Q-Q/A-K2/D2-O/J-K1/D1-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-D2/K2-J/O-D1/K1 (AK2JK1A'G2D2OD1G1,C1,C2|Q,Q')

Solution 64: A/Q-Q/A-K2/D2-O/J-K1/D1-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-D2/K2-J/O-D1/K1
64a: A'/Q'-Q/A-K2/D2-O/J-K1/D1-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-D2/K2-J/O-D1/K1 (AK2JK1,A'B2H2D2OD1H1B1|QQ')
64b: A/Q-Q/A-K2/D2-O/J-K1/D1-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-D2/K2-J/O-D1/K1 (AK2JK1A'B2H2D2OD1H1B1|Q,Q')

Solution 65: A/Q-Q/A-K2/D2-O/J-K1/D1-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-D2/K2-J/O-D1/K1
65a: A'/Q'-Q/A-K2/D2-O/J-K1/D1-J'/O'-B1/B1 | A/Q-Q'/A'-B2/B2-O'/J'-D2/K2-J/O-D1/K1 (AK2JK1,A'B2O'B1,D1J'D2O|QQ')
65b: A'/Q'-Q/A-K2/D2-O'/J'-K1/D1-J'/O'-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-D2/K2-J/O-D1/K1 (AK2JD2O'B1A'B2OD1J'K1|QQ')
65c: A/Q-Q/A-K2/D2-O/J-K1/D1-J'/O'-B1/B1 | A'/Q'-Q'/A'-B2/B2-O'/J'-D2/K2-J/O-D1/K1 (AK2JK1A'B2O'B1,D1J'D2O|Q,Q')
65d: A/Q-Q/A-K2/D2-O'/J'-K1/D1-J'/O'-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-D2/K2-J/O-D1/K1 (AK2JD2O'B1,A'B2OD1J'K1|Q,Q')

Solution 66: A/Q-Q/A-K2/D2-O/J-D2/K2-G1/C1-C1/G1 | A/Q-Q/A-G2/C2-C2/G2-K1/D1-J/O-D1/K1
66a: A'/Q'-Q/A-K2/D2-O/J-D2/K2-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-K1/D1-J/O-D1/K1 (AK2G1A'G2K1,C1,D1JD2O,C2|QQ')
66b: A/Q-Q/A-K2/D2-O/J-D2/K2-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-K1/D1-J/O-D1/K1 (AK2G1,A'G2K1,C1,D1JD2O,C2|Q,Q')

Solution 67: A/Q-Q/A-K2/D2-O/J-D2/K2-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-K1/D1-J/O-D1/K1
67a: A'/Q'-Q/A-K2/D2-O/J-D2/K2-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-K1/D1-J/O-D1/K1 (AK2H1B1A'B2H2K1,D1JD2O|QQ')
67b: A/Q-Q/A-K2/D2-O/J-D2/K2-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-K1/D1-J/O-D1/K1 (AK2H1B1,A'B2H2K1,D1JD2O|Q,Q')

Solution 68: A/Q-Q/A-K2/D2-O/J-D2/K2-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-K1/D1-J/O-D1/K1
68a: A'/Q'-Q/A-K2/D2-O'/J'-D2/K2-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-K1/D1-J'/O'-D1/K1 (AK2JK1,A'B2OB1,D1J'D2O'|QQ')
68b: A'/Q'-Q/A-K2/D2-O/J-D2/K2-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O'/J'-K1/D1-J'/O'-D1/K1 (AK2JD2OB1A'B2O'D1J'K1|QQ')
68c: A/Q-Q/A-K2/D2-O'/J'-D2/K2-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-K1/D1-J'/O'-D1/K1 (AK2JK1A'B2OB1,D1J'D2O'|Q,Q')
68d (chiral): A/Q-Q/A-K2/D2-O/J-D2/K2-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O'/J'-K1/D1-J'/O'-D1/K1 (AK2JD2OB1|Q)/(A'B2O'D1J'K1|Q')

Solution 69: A/Q-Q/A-K2/D2-H2/H2-K1/D1-G1/C1-C1/G1 | A/Q-Q/A-G2/C2-C2/G2-D2/K2-H1/H1-D1/K1
69a: A'/Q'-Q/A-K2/D2-H2/H2-K1/D1-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-D2/K2-H1/H1-D1/K1 (AK2H1D1G1A'G2D2H2K1,C1,C2|QQ')
69b: A/Q-Q/A-K2/D2-H2/H2-K1/D1-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-D2/K2-H1/H1-D1/K1 (AK2H1D1G1,A'G2D2H2K1,C1,C2|Q,Q')

Solution 70: A/Q-Q/A-K2/D2-H2/H2-K1/D1-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-D2/K2-H1/H1-D1/K1
70a: A'/Q'-Q/A-K2/D2-H2'/H2'-K1/D1-H1'/H1'-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-D2/K2-H1/H1-D1/K1 (AK2H1D1H1'B1A'B2H2D2H2'K1|QQ')
70a: A'/Q'-Q/A-K2/D2-H2'/H2-K1/D1-H1'/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2'-D2/K2-H1/H1'-D1/K1 (AK2H1B1A'B2H2K1,D1H1',D2H2'|QQ')
70a: A/Q-Q/A-K2/D2-H2'/H2'-K1/D1-H1'/H1'-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-D2/K2-H1/H1-D1/K1 (AK2H1D1H1'B1,A'B2H2D2H2'K1|Q,Q')
70a: A/Q-Q/A-K2/D2-H2'/H2-K1/D1-H1'/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2'-D2/K2-H1/H1'-D1/K1 (AK2H1B1,A'B2H2K1,D1H1',D2H2'|Q,Q')

Solution 71: A/Q-Q/A-K2/D2-H2/H2-K1/D1-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-D2/K2-H1/H1-D1/K1
71a: A'/Q'-Q/A-K2/D2-H2/H2-K1/D1-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-D2/K2-H1/H1-D1/K1 (AK2H1D1JD2H2K1,A'B2OB1|QQ')
71b: A/Q-Q/A-K2/D2-H2/H2-K1/D1-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-D2/K2-H1/H1-D1/K1 (AK2H1D1JD2H2K1A'B2OB1|Q,Q')

Solution 72: A/Q-Q/A-K2/D2-H2/H2-D2/K2-G1/C1-C1/G1 | A/Q-Q/A-G2/C2-C2/G2-K1/D1-H1/H1-D1/K1
72a: A'/Q'-Q/A-K2/D2-H2/H2-D2/K2-G1/C1-C1/G1 | A/Q-Q'/A'-G2/C2-C2/G2-K1/D1-H1/H1-D1/K1 (AK2G1A'G2K1,C1,D1H1,D2H2,C2|QQ')
72b (chiral): A/Q-Q/A-K2/D2-H2/H2-D2/K2-G1/C1-C1/G1 | A'/Q'-Q'/A'-G2/C2-C2/G2-K1/D1-H1/H1-D1/K1 (AK2G1,C1,D2H2|Q)/(A'G2K1,D1H1,C2|Q')

Solution 73: A/Q-Q/A-K2/D2-H2/H2-D2/K2-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-K1/D1-H1/H1-D1/K1
73a: A'/Q'-Q/A-K2/D2-H2'/H2'-D2/K2-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-K1/D1-H1'/H1'-D1/K1 (AK2H1B1A'B2H2K1,D1H1',D2H2'|QQ')
73b: A'/Q'-Q/A-K2/D2-H2'/H2-D2/K2-H1/H1'-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2'-K1/D1-H1'/H1-D1/K1 (AK2H1D1H1'B1A'B2H2D2H2'K1|QQ')
73c (chiral): A/Q-Q/A-K2/D2-H2'/H2'-D2/K2-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-K1/D1-H1'/H1'-D1/K1 (AK2H1B1,D2H2'|Q)/(A'B2H2K1,D1H1'|Q')
73d: A/Q-Q/A-K2/D2-H2'/H2-D2/K2-H1/H1'-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2'-K1/D1-H1'/H1-D1/K1 (AK2H1D1H1'B1,A'B2H2D2H2'K1|Q,Q')

Solution 74: A/Q-Q/A-K2/D2-H2/H2-D2/K2-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-K1/D1-H1/H1-D1/K1
74a: A'/Q'-Q/A-K2/D2-H2/H2-D2/K2-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-K1/D1-H1/H1-D1/K1 (AK2JK1,A'B2OB1,D1H1,D2H2|QQ')
74b: A/Q-Q/A-K2/D2-H2/H2-D2/K2-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-K1/D1-H1/H1-D1/K1 (AK2JK1A'B2OB1,D1H1,D2H2|Q,Q')

Solution 75: A/Q-Q/A-K2/D2-C2/G2-K1/D1-H1/H1-C1/G1 | A/Q-Q/A-G2/C2-H2/H2-D2/K2-G1/C1-D1/K1
75a: A'/Q'-Q/A-K2/D2-C2/G2-K1/D1-H1/H1-C1/G1 | A/Q-Q'/A'-G2/C2-H2/H2-D2/K2-G1/C1-D1/K1 (AK2G1A'G2K1,C1D1H1,D2C2H2|QQ')
75b: A/Q-Q/A-K2/D2-C2/G2-K1/D1-H1/H1-C1/G1 | A'/Q'-Q'/A'-G2/C2-H2/H2-D2/K2-G1/C1-D1/K1 (AK2G1,A'G2K1,C1D1H1,D2C2H2|Q,Q')

Solution 76: A/Q-Q/A-K2/D2-C2/G2-K1/D1-J/O-C1/G1 | A/Q-Q/A-G2/C2-O/J-D2/K2-G1/C1-D1/K1
76a: A'/Q'-Q/A-K2/D2-C2/G2-K1/D1-J/O-C1/G1 | A/Q-Q'/A'-G2/C2-O/J-D2/K2-G1/C1-D1/K1 (AK2G1A'G2K1,D1JD2C2OC1|QQ')
76b: A/Q-Q/A-K2/D2-C2/G2-K1/D1-J/O-C1/G1 | A'/Q'-Q'/A'-G2/C2-O/J-D2/K2-G1/C1-D1/K1 (AK2G1,A'G2K1,D1JD2C2OC1|Q,Q')

Solution 77: A/Q-Q/A-K2/D2-C2/G2-D2/K2-H1/H1-C1/G1 | A/Q-Q/A-G2/C2-H2/H2-K1/D1-G1/C1-D1/K1
77a: A'/Q'-Q/A-K2/D2-C2/G2-D2/K2-H1/H1-C1/G1 | A/Q-Q'/A'-G2/C2-H2/H2-K1/D1-G1/C1-D1/K1 (AK2H1C1D1G1A'G2D2C2H2K1|QQ')
77b: A/Q-Q/A-K2/D2-C2/G2-D2/K2-H1/H1-C1/G1 | A'/Q'-Q'/A'-G2/C2-H2/H2-K1/D1-G1/C1-D1/K1 (AK2H1C1D1G1,A'G2D2C2H2K1|Q,Q')

Solution 78: A/Q-Q/A-K2/D2-C2/G2-D2/K2-J/O-C1/G1 | A/Q-Q/A-G2/C2-O/J-K1/D1-G1/C1-D1/K1
78a: A'/Q'-Q/A-K2/D2-C2/G2-D2/K2-J/O-C1/G1 | A/Q-Q'/A'-G2/C2-O/J-K1/D1-G1/C1-D1/K1 (AK2JK1,A'G2D2C2OC1D1G1|QQ')
78b: A/Q-Q/A-K2/D2-C2/G2-D2/K2-J/O-C1/G1 | A'/Q'-Q'/A'-G2/C2-O/J-K1/D1-G1/C1-D1/K1 (AK2JK1A'G2D2C2OC1D1G1|Q,Q')

Solution 79: A/Q-Q/A-G2/C2-O/J-M/M-G1/C1-B1/B1 | A/Q-Q/A-B2/B2-C2/G2-M/M-J/O-C1/G1
79a: A'/Q'-Q/A-G2/C2-O/J-M'/M-G1/C1-B1/B1 | A/Q-Q'/A'-B2/B2-C2/G2-M/M'-J/O-C1/G1 (AG2MG1,A'B2C2OC1B1,JM'|QQ')
79b: A'/Q'-Q/A-G2/C2-O/J-M'/M'-G1/C1-B1/B1 | A/Q-Q'/A'-B2/B2-C2/G2-M/M-J/O-C1/G1 (AG2MJM'G1,A'B2C2OC1B1|QQ')
79c: A/Q-Q/A-G2/C2-O/J-M'/M-G1/C1-B1/B1 | A'/Q'-Q'/A'-B2/B2-C2/G2-M/M'-J/O-C1/G1 (AG2MG1A'B2C2OC1B1,JM'|Q,Q')
79d: A/Q-Q/A-G2/C2-O/J-M'/M'-G1/C1-B1/B1 | A'/Q'-Q'/A'-B2/B2-C2/G2-M/M-J/O-C1/G1 (AG2MJM'G1A'B2C2OC1B1|Q,Q')

Solution 80: A/Q-Q/A-G2/C2-L2/I2-L1/I1-G1/C1-B1/B1 | A/Q-Q/A-B2/B2-C2/G2-I2/L2-I1/L1-C1/G1
80a: A'/Q'-Q/A-G2/C2-L2/I2-L1/I1-G1/C1-B1/B1 | A/Q-Q'/A'-B2/B2-C2/G2-I2/L2-I1/L1-C1/G1 (AG2I2L1C1B1A'B2C2L2I1G1|QQ')
80b: A/Q-Q/A-G2/C2-L2/I2-L1/I1-G1/C1-B1/B1 | A'/Q'-Q'/A'-B2/B2-C2/G2-I2/L2-I1/L1-C1/G1 (AG2I2L1C1B1,A'B2C2L2I1G1|Q,Q')

Solution 81: A/Q-Q/A-G2/C2-L2/I2-I2/L2-G1/C1-B1/B1 | A/Q-Q/A-B2/B2-C2/G2-L1/I1-I1/L1-C1/G1
81a: A'/Q'-Q/A-G2/C2-L2/I2-I2/L2-G1/C1-B1/B1 | A/Q-Q'/A'-B2/B2-C2/G2-L1/I1-I1/L1-C1/G1 (AG2L1C1B1A'B2C2L2G1,I1,I2|QQ')
81b: A/Q-Q/A-G2/C2-L2/I2-I2/L2-G1/C1-B1/B1 | A'/Q'-Q'/A'-B2/B2-C2/G2-L1/I1-I1/L1-C1/G1 (AG2L1C1B1,A'B2C2L2G1,I1,I1|Q,Q')

Solution 82: A/Q-Q/A-G2/C2-H2/H2-M/M-G1/C1-B1/B1 | A/Q-Q/A-B2/B2-C2/G2-M/M-H1/H1-C1/G1
82a: A'/Q'-Q/A-G2/C2-H2/H2-M'/M-G1/C1-B1/B1 | A/Q-Q'/A'-B2/B2-C2/G2-M/M'-H1/H1-C1/G1 (AG2MG1,A'B2C2H2M'H1C1B1|QQ')
82a: A'/Q'-Q/A-G2/C2-H2/H2-M'/M'-G1/C1-B1/B1 | A/Q-Q'/A'-B2/B2-C2/G2-M/M-H1/H1-C1/G1 (AG2MH1C1B1A'B2C2H2M'G1|QQ')
82a: A/Q-Q/A-G2/C2-H2/H2-M'/M-G1/C1-B1/B1 | A'/Q'-Q'/A'-B2/B2-C2/G2-M/M'-H1/H1-C1/G1 (AG2MG1A'B2C2H2M'H1C1B1|Q,Q')
82a: A/Q-Q/A-G2/C2-H2/H2-M'/M'-G1/C1-B1/B1 | A'/Q'-Q'/A'-B2/B2-C2/G2-M/M-H1/H1-C1/G1 (AG2MH1C1B1,A'B2C2H2M'G1|Q,Q')

Solution 83: A/Q-Q/A-G2/C2-C2/G2-L1/I1-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-I2/L2-G1/C1-C1/G1
83a: A'/Q'-Q/A-G2/C2-C2/G2-L1/I1-I1/L1-B1/B1 | A/Q-Q'/A'-B2/B2-L2/I2-I2/L2-G1/C1-C1/G1 (AG2L1B1A'B2L2G1,C1,I1,I2,C2|QQ')
83b (chiral): A/Q-Q/A-G2/C2-C2/G2-L1/I1-I1/L1-B1/B1 | A'/Q'-Q'/A'-B2/B2-L2/I2-I2/L2-G1/C1-C1/G1 (AG2L1B1,I1,C2|Q)/(A'B2L2G1,C1,I2|Q')

Solution 84: A/Q-Q/A-G2/C2-C2/G2-M/M-G1/C1-C1/G1 (AG2MG1,C1,C2|Q)

Solution 85: A/Q-Q/A-G2/C2-C2/G2-M/M-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-M/M-G1/C1-C1/G1
85a: A'/Q'-Q/A-G2/C2-C2/G2-M/M'-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-M'/M-G1/C1-C1/G1 (AG2MG1,A'B2H2M'H1B1,C1,C2|QQ')
85b: A'/Q'-Q/A-G2/C2-C2/G2-M/M-H1/H1-B1/B1 | A/Q-Q'/A'-B2/B2-H2/H2-M'/M'-G1/C1-C1/G1 (AG2MH1B1A'B2H2M'G1,C1,C2|QQ')
85c: A/Q-Q/A-G2/C2-C2/G2-M/M'-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-M'/M-G1/C1-C1/G1 (AG2MG1A'B2H2M'H1B1,C1,C2|Q,Q')
85d: A/Q-Q/A-G2/C2-C2/G2-M/M-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2/B2-H2/H2-M'/M'-G1/C1-C1/G1 (AG2MH1B1,A'B2H2M'G1,C1,C2|Q,Q')

Solution 86: A/Q-Q/A-G2/C2-C2/G2-M/M-J/O-B1/B1 | A/Q-Q/A-B2/B2-O/J-M/M-G1/C1-C1/G1
86a: A'/Q'-Q/A-G2/C2-C2/G2-M/M'-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M'/M-G1/C1-C1/G1 (AG2MG1,A'B2OB1,C1,JM',C2|QQ')
86b: A'/Q'-Q/A-G2/C2-C2/G2-M/M-J/O-B1/B1 | A/Q-Q'/A'-B2/B2-O/J-M'/M'-G1/C1-C1/G1 (AG2MJM'G1,A'B2OB1,C1,C2|QQ')
86c: A/Q-Q/A-G2/C2-C2/G2-M/M'-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M'/M-G1/C1-C1/G1 (AG2MG1A'B2OB1,C1,JM',C2|Q,Q')
86d: A/Q-Q/A-G2/C2-C2/G2-M/M-J/O-B1/B1 | A'/Q'-Q'/A'-B2/B2-O/J-M'/M'-G1/C1-C1/G1 (AG2MJM'G1A'B2OB1,C1,C2|Q,Q')

Solution 87: A/Q-Q/A-G2/C2-C2/G2-I2/L2-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-L1/I1-G1/C1-C1/G1
87a: A'/Q'-Q/A-G2/C2-C2/G2-I2/L2-I1/L1-B1/B1 | A/Q-Q'/A'-B2/B2-L2/I2-L1/I1-G1/C1-C1/G1 (AG2I2L1B1A'B2L2I1G1,C1,C2|QQ')
87b: A/Q-Q/A-G2/C2-C2/G2-I2/L2-I1/L1-B1/B1 | A'/Q'-Q'/A'-B2/B2-L2/I2-L1/I1-G1/C1-C1/G1 (AG2I2L1B1,A'B2L2I1G1,C1,C2|Q,Q')

Solution 88: A/Q-Q/A-B2/B2-O/J-L1/I1-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-I2/L2-J/O-B1/B1
88a: A'/Q'-Q/A-B2/B2-O/J-L1/I1-I1/L1-B1'/B1' | A/Q-Q'/A'-B2'/B2'-L2/I2-I2/L2-J/O-B1/B1 (AB2OB1,A'B2'L2JL1B1',I1,I2|QQ')
88b: A'/Q'-Q/A-B2/B2'-O/J-L1/I1-I1/L1-B1/B1' | A/Q-Q'/A'-B2'/B2-L2/I2-I2/L2-J/O-B1'/B1 (AB2L2JL1B1,A'B2'OB1',I1,I2|QQ')
88c: A/Q-Q/A-B2/B2-O/J-L1/I1-I1/L1-B1'/B1' | A'/Q'-Q'/A'-B2'/B2'-L2/I2-I2/L2-J/O-B1/B1 (AB2OB1A'B2'L2JL1B1',I1,I2|Q,Q')
88d: A/Q-Q/A-B2/B2'-O/J-L1/I1-I1/L1-B1/B1' | A'/Q'-Q'/A'-B2'/B2-L2/I2-I2/L2-J/O-B1'/B1 (AB2L2JL1B1A'B2'OB1',I1,I2|Q,Q')

Solution 89: A/Q-Q/A-B2/B2-O/J-M/M-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-M/M-J/O-B1/B1
89a: A'/Q'-Q/A-B2/B2-O/J-M'/M-H1/H1-B1'/B1' | A/Q-Q'/A'-B2'/B2'-H2/H2-M/M'-J/O-B1/B1 (AB2OB1,A'B2'H2MH1B1',JM'|QQ')
89b: A'/Q'-Q/A-B2/B2-O/J-M'/M'-H1/H1-B1'/B1' | A/Q-Q'/A'-B2'/B2'-H2/H2-M/M-J/O-B1/B1 (AB2OB1,A'B2'H2MJM'H1B1'|QQ')
89c: A'/Q'-Q/A-B2/B2'-O/J-M'/M-H1/H1-B1/B1' | A/Q-Q'/A'-B2'/B2-H2/H2-M/M'-J/O-B1'/B1 (AB2H2MH1B1,A'B2'OB1',JM'|QQ')
89d: A'/Q'-Q/A-B2/B2'-O/J-M'/M'-H1/H1-B1/B1' | A/Q-Q'/A'-B2'/B2-H2/H2-M/M-J/O-B1'/B1 (AB2H2MJM'H1B1,A'B2'OB1'|QQ')
89e: A/Q-Q/A-B2/B2-O/J-M'/M-H1/H1-B1'/B1' | A'/Q'-Q'/A'-B2'/B2'-H2/H2-M/M'-J/O-B1/B1 (AB2OB1A'B2'H2MH1B1',JM'|Q,Q')
89f: A/Q-Q/A-B2/B2-O/J-M'/M'-H1/H1-B1'/B1' | A'/Q'-Q'/A'-B2'/B2'-H2/H2-M/M-J/O-B1/B1 (AB2OB1A'B2'H2MJM'H1B1'|Q,Q')
89g: A/Q-Q/A-B2/B2'-O/J-M'/M-H1/H1-B1/B1' | A'/Q'-Q'/A'-B2'/B2-H2/H2-M/M'-J/O-B1'/B1 (AB2H2MH1B1A'B2OB1',JM'|Q,Q')
89h: A/Q-Q/A-B2/B2'-O/J-M'/M'-H1/H1-B1/B1' | A'/Q'-Q'/A'-B2'/B2-H2/H2-M/M-J/O-B1'/B1 (AB2H2MJM'H1B1A'B2'OB1'|Q,Q')

Solution 90: A/Q-Q/A-B2/B2-O/J-M/M-J/O-B1/B1 (AB2OB1,JM|Q)

Solution 91: A/Q-Q/A-B2/B2-O/J-I2/L2-I1/L1-B1/B1 | A/Q-Q/A-B2/B2-L2/I2-L1/I1-J/O-B1/B1
91a: A'/Q'-Q/A-B2/B2-O/J-I2/L2-I1/L1-B1'/B1' | A/Q-Q'/A'-B2'/B2'-L2/I2-L1/I1-J/O-B1/B1 (AB2OB1,A'B2'L2I1JI2L1B1'|QQ')
91b: A'/Q'-Q/A-B2/B2'-O/J-I2/L2-I1/L1-B1/B1' | A/Q-Q'/A'-B2'/B2-L2/I2-L1/I1-J/O-B1'/B1 (AB2L2I1JI2L1B1,A'B2'OB1'|QQ')
91c: A/Q-Q/A-B2/B2-O/J-I2/L2-I1/L1-B1'/B1' | A'/Q'-Q'/A'-B2'/B2'-L2/I2-L1/I1-J/O-B1/B1 (AB2OB1A'B2'L2I1JI2L1B1'|Q,Q')
91d: A/Q-Q/A-B2/B2'-O/J-I2/L2-I1/L1-B1/B1' | A'/Q'-Q'/A'-B2'/B2-L2/I2-L1/I1-J/O-B1'/B1 (AB2L2I1JI2L1B1A'B2'OB1'|Q,Q')

Solution 92: A/Q-Q/A-B2/B2-L2/I2-L1/I1-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-I2/L2-I1/L1-B1/B1
92a: A'/Q'-Q/A-B2/B2-L2/I2-L1/I1-H1/H1-B1/B1 | A/Q-Q'/A'-B2'/B2'-H2/H2-I2/L2-I1/L1-B1'/B1' (AB2L2I1H1B1A'B2'H2I2L1B1'|QQ')
92b: A'/Q'-Q/A-B2/B2'-L2/I2-L1/I1-H1/H1-B1'/B1 | A/Q-Q'/A'-B2'/B2-H2/H2-I2/L2-I1/L1-B1/B1' (AB2H2I2L1B1A'B2'L2I1H1B1'|QQ')
92c: A/Q-Q/A-B2/B2-L2/I2-L1/I1-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2'/B2'-H2/H2-I2/L2-I1/L1-B1'/B1' (AB2L2I1H1B1,A'B2'H2I2L1B1'|Q,Q')
92d: A/Q-Q/A-B2/B2'-L2/I2-L1/I1-H1/H1-B1'/B1 | A'/Q'-Q'/A'-B2'/B2-H2/H2-I2/L2-I1/L1-B1/B1' (AB2H2I2L1B1,A'B2'L2I1H1B1'|Q,Q')

Solution 93: A/Q-Q/A-B2/B2-L2/I2-I2/L2-H1/H1-B1/B1 | A/Q-Q/A-B2/B2-H2/H2-L1/I1-I1/L1-B1/B1
93a: A'/Q'-Q/A-B2/B2-L2/I2-I2/L2-H1/H1-B1/B1 | A/Q-Q'/A'-B2'/B2'-H2/H2-L1/I1-I1/L1-B1'/B1' (AB2L2H1B1A'B2'H2L1B1',I1,I2|QQ')
93b: A'/Q'-Q/A-B2/B2'-L2/I2-I2/L2-H1/H1-B1'/B1 | A/Q-Q'/A'-B2'/B2-H2/H2-L1/I1-I1/L1-B1/B1' (AB2H2L1B1A'B2'L2H1B1',I1,I2|QQ')
93c: A/Q-Q/A-B2/B2-L2/I2-I2/L2-H1/H1-B1/B1 | A'/Q'-Q'/A'-B2'/B2'-H2/H2-L1/I1-I1/L1-B1'/B1' (AB2L2H1B1,A'B2'H2L1B1',I1,I2|Q,Q')
93d: A/Q-Q/A-B2/B2'-L2/I2-I2/L2-H1/H1-B1'/B1 | A'/Q'-Q'/A'-B2'/B2-H2/H2-L1/I1-I1/L1-B1/B1' (AB2H2L1B1,A'B2'L2H1B1',I1,I2|Q,Q')

Solution 94: A/Q-Q/A-B2/B2-H2/H2-M/M-H1/H1-B1/B1 (AB2H2MH1B1|Q)

2|a: 13

3|a: 57b, 60d, 75b

4|a: 8b, 11c, 34, 44b, 45b, 67b, 70d, 73c, 83b, 84, 90
4|a, 2|b: 1a, 3a, 5a, 6a, 8a, 9a, 11a, 12a, 12b, 18a, 27a, 32a, 35a, 42a, 65a, 68a, 74a, 86a

5|a: 46b, 47d, 69b, 81b, 85d, 87b, 93c, 93d

6|a: 1b, 2c, 2d, 3d, 4b, 5b, 9c, 12e, 22b, 35d, 39b, 41c, 42c, 48d, 50, 51b, 52b, 55d, 58b, 59b, 60c, 61b, 62d, 65d, 68d, 70c, 72b, 73d, 76b, 77b, 80b, 82d, 92c, 92d, 94
6|a, 2|b: 7a, 9b, 10a, 11b, 12c, 14a, 16a, 24a, 26a, 29a, 38b, 48a, 55b, 56a, 57a, 58a, 60a, 60b, 72a, 75a, 76a, 79b

8|a: 7b, 9d, 10c, 12g, 12h, 14c, 21b, 24b, 29c, 30b, 33f, 33h, 36c, 38d, 65c, 68c, 74b, 86c
8|a, 2|b: 10b, 14b, 15a, 17a, 19a, 21a, 25a, 28a, 31a, 32b, 40a, 44a, 45a, 49b, 53a, 54a, 62a, 64a, 67a, 70b, 71a, 73a, 78a, 82a, 83a, 89b, 89d, 91a, 91b

10|a: 10d, 14d, 15b, 17b, 19b, 25b, 28b, 31b, 32d, 40b, 47c, 49c, 63b, 79c, 85c, 86d, 88c, 88d, 89e, 89g
10|a, 2|b: 6b, 18b, 20a, 23a, 29b, 33a, 33c, 36b, 37a, 38a, 41b, 43a, 46a, 47b, 69a, 81a, 85b, 87a, 93a, 93b

12|a: 3c, 6c, 6d, 11d, 12f, 16b, 18c, 18d, 20b, 23b, 26b, 27b, 29d, 32c, 33e, 33g, 35c, 36d, 37b, 38c, 41d, 42c, 43b, 48c, 49d, 53b, 54b, 55c, 56b, 62c, 64b, 66b, 71b, 78b, 79d, 82c, 89f, 89h, 91c, 91d
12|a, 2|b: 2a, 2b, 3b, 4a, 12d, 22a, 30a, 33b, 33d, 35b, 36a, 39a, 41a, 42b, 47a, 48b, 49a, 51a, 52a, 55a, 59a, 61a, 62b, 63a, 65b, 66a, 68b, 70a, 73b, 77a, 79a, 80a, 82b, 85a, 86b, 88a, 88b, 89a, 89c, 92a, 92b
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sun Apr 05, 2015 9:16 pm

AAAAAAB example: three distinct 3,3,3,3,3,3,3A colorings
Attachments
3_7_57b.png
(48.58 KiB) Not downloaded yet
3_7_60d.png
(48.13 KiB) Not downloaded yet
3_7_75b.png
(48.65 KiB) Not downloaded yet
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Sun Apr 05, 2015 9:56 pm

I also gave some thought to symmetries of these tilings. There are three kinds of rotational symmetries:

Rotations through vertex -- these require the vertex sequence to be periodic. For example, vertex of type ABABAB has 3-fold rotational symmetry.
Rotations through center of a polygon -- These require the polygon in question to be periodic, i.e. to have more sides than specified in the solution. The AD square in AAAB type has a 2-fold rotational symmetry because it has 4 sides but its description has only 2.
180-degree rotations through center of an edge -- These can be derived directly from the solution; Whenever there's an a symbol like B1/B1, it signifies that the B1 edge has a center of rotation. Note that apostrophes DO matter -- a B1/B1' edge does NOT have a center of rotation.

As for reflections, those are a bit harder, but they can be also derived from the solution.
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Mon Apr 06, 2015 6:17 pm

Type AAAAABB:

Edge data:
Code: Select all
a b b b a
a       a
a a A a a : A xM -K,I2,F2,B1

b b a a a
a       a
a a A b b : B1 xB1 -A

b b a a a
a       b
a a A a b : C1 xF1 -B1,C1,D1,E

b b a a b
a       b
a a A a a : D1 xI1 -F1,G1,H,D2

b b a b b
a       a
a a A a a : E xK -I1,J,G2,C2

b a a a a
b       a
a a A b b : F1 xC1 -A

b a a a a
b       b
a a A a b : G1 xG1 -B1,C1,D1,E

b a a a b
b       b
a a A a a : H xJ -F1,G1,H,D2

b a a b b
b       a
a a A a a : D2 xI2 -I1,J,G2,C2

a a a a a
b       a
b a A b b : I1 xD1 -A

a a a a a
b       b
b a A a b : J xH -B1,C1,D1,E

a a a a b
b       b
b a A a a : G2 xG2 -F1,G1,H,D2

a a a b b
b       a
b a A a a : C2 xF2 -I1,J,G2,C2

a a a a a
a       a
b b A b b : K xE -A

a a a a a
a       b
b b A a b : I2 xD2 -B1,C1,D1,E

a a a a b
a       b
b b A a a : F2 xC2 -F1,G1,H,D2

a a a b b
a       a
b b A a a : B2 xB2 -I1,J,G2,C2

a a b a a
a       a
a a B a a : L xL -M

a a a a a
a       a
a b B b b : M xA -L


Vertex sequence:
A/M
L/L
M/A
K/E I2/D2 F2/C2 B2/B2
I1/D1 J/H G2/G2 C2/F2
F1/C1 G1/G1 H/J D2/I2
B1/B1 C1/F1 D1/I1 E/K

256 possible sequences, leading to 30 basic solutions:

Solution 1: A/M-L/L-M/A-K/E-I1/D1-G1/G1-D1/I1 | A/M-L/L-M/A-I2/D2-G2/G2-D2/I2-E/K
1a: A'/M'-L'/L-M/A-K/E-I1/D1-G1/G1-D1/I1 | A/M-L/L'-M'/A'-I2/D2-G2/G2-D2/I2-E/K (AK,A'I2EI1,D1G1,D2G2|LM,L'M')
1b: A'/M'-L/L-M/A-K/E-I1/D1-G1/G1-D1/I1 | A/M-L'/L'-M'/A'-I2/D2-G2/G2-D2/I2-E/K (AK,A'I2EI1,D1G1,D2G2|LML'M')
1c: A/M-L/L-M/A-K/E-I1/D1-G1/G1-D1/I1 | A'/M'-L'/L'-M'/A'-I2/D2-G2/G2-D2/I2-E/K (AKA'I2EI1,D1G1,D2G2|LM,L'M')
1d: A/M-L'/L-M/A-K/E-I1/D1-G1/G1-D1/I1 | A'/M'-L/L'-M'/A'-I2/D2-G2/G2-D2/I2-E/K (AKA'I2EI1,D1G1,D2G2|LML'M')

Solution 2: A/M-L/L-M/A-K/E-I1/D1-H/J-D1/I1 | A/M-L/L-M/A-I2/D2-J/H-D2/I2-E/K
2a: A'/M'-L'/L-M/A-K/E-I1/D1-H/J-D1/I1 | A/M-L/L'-M'/A'-I2/D2-J/H-D2/I2-E/K (AK,A'I2EI1,D1HD2J|LM,L'M')
2b: A'/M'-L/L-M/A-K/E-I1/D1-H/J-D1/I1 | A/M-L'/L'-M'/A'-I2/D2-J/H-D2/I2-E/K (AK,A'I2EI1,D1HD2J|LML'M')
2c: A/M-L/L-M/A-K/E-I1/D1-H/J-D1/I1 | A'/M'-L'/L'-M'/A'-I2/D2-J/H-D2/I2-E/K (AKA'I2EI1,D1HD2J|LM,L'M')
2d: A/M-L'/L-M/A-K/E-I1/D1-H/J-D1/I1 | A'/M'-L/L'-M'/A'-I2/D2-J/H-D2/I2-E/K (AKA'I2EI1,D1HD2J|LML'M')

Solution 3: A/M-L/L-M/A-K/E-J/H-F1/C1-C1/F1 | A/M-L/L-M/A-F2/C2-C2/F2-H/J-E/K
3a: A'/M'-L'/L-M/A-K/E-J/H-F1/C1-C1/F1 | A/M-L/L'-M'/A'-F2/C2-C2/F2-H/J-E/K (AK,A'F2HF1,C1,EJ,C2|LM,L'M')
3b: A'/M'-L/L-M/A-K/E-J/H-F1/C1-C1/F1 | A/M-L'/L'-M'/A'-F2/C2-C2/F2-H/J-E/K (AK,A'F2HF1,C1,EJ,C2|LML'M')
3c: A/M-L/L-M/A-K/E-J/H-F1/C1-C1/F1 | A'/M'-L'/L'-M'/A'-F2/C2-C2/F2-H/J-E/K (AKA'F2HF1,C1,EJ,C2|LM,L'M')
3d: A/M-L'/L-M/A-K/E-J/H-F1/C1-C1/F1 | A'/M'-L/L'-M'/A'-F2/C2-C2/F2-H/J-E/K (AKA'F2HF1,C1,EJ,C2|LML'M')

Solution 4: A/M-L/L-M/A-K/E-J/H-G1/G1-B1/B1 | A/M-L/L-M/A-B2/B2-G2/G2-H/J-E/K
4a: A'/M'-L'/L-M/A-K/E-J/H-G1/G1-B1/B1 | A/M-L/L'-M'/A'-B2/B2-G2/G2-H/J-E/K (AK,A'B2G2HG1B1,EJ|LM,L'M')
4a: A'/M'-L/L-M/A-K/E-J/H-G1/G1-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-G2/G2-H/J-E/K (AK,A'B2G2HG1B1,EJ|LML'M')
4a: A/M-L/L-M/A-K/E-J/H-G1/G1-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-G2/G2-H/J-E/K (AKA'B2G2HG1B1,EJ|LM,L'M')
4a: A/M-L'/L-M/A-K/E-J/H-G1/G1-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-G2/G2-H/J-E/K (AKA'B2G2HG1B1,EJ|LML'M')

Solution 5: A/M-L/L-M/A-K/E-J/H-G1/G1-E/K | A/M-L/L-M/A-K/E-G2/G2-H/J-E/K
5a: A'/M'-L'/L-M/A-K/E-J/H-G1/G1-E'/K' | A/M-L/L'-M'/A'-K'/E'-G2/G2-H/J-E/K (AK,A'K',EJ,E'G2HG1|LM,L'M')
5b: A'/M'-L/L-M/A-K/E-J/H-G1/G1-E'/K' | A/M-L'/L'-M'/A'-K'/E'-G2/G2-H/J-E/K (AK,A'K',EJ,E'G2HG1|LML'M')
5c: A'/M'-L'/L-M/A-K/E-J/H-G1/G1-E/K | A/M-L/L'-M'/A'-K'/E'-G2/G2-H/J-E'/K' (AKA'K',EJE'G2HG1|LM,L'M')
5d: A'/M'-L/L-M/A-K/E-J/H-G1/G1-E/K | A/M-L'/L'-M'/A'-K'/E'-G2/G2-H/J-E'/K' (AKA'K',EJE'G2HG1|LML'M')
5e: A/M-L/L-M/A-K/E-J/H-G1/G1-E/K | A'/M'-L'/L'-M'/A'-K'/E'-G2/G2-H/J-E'/K' (AK,A'K',EJE'G2HG1|LM,L'M')
5f: A/M-L'/L-M/A-K/E-J/H-G1/G1-E/K | A'/M'-L/L'-M'/A'-K'/E'-G2/G2-H/J-E'/K' (AK,A'K',EJE'G2HG1|LML'M')
5g: A/M-L/L-M/A-K/E-J/H-G1/G1-E'/K' | A'/M'-L'/L'-M'/A'-K'/E'-G2/G2-H/J-E/K (AKA'K',EJ,E'G2HG1|LM,L'M')
5h: A/M-L'/L-M/A-K/E-J/H-G1/G1-E'/K' | A'/M'-L/L'-M'/A'-K'/E'-G2/G2-H/J-E/K (AKA'K',EJ,E'G2HG1|LML'M')

Solution 6: A/M-L/L-M/A-K/E-J/H-H/J-B1/B1 | A/M-L/L-M/A-B2/B2-J/H-H/J-E/K
6a: A'/M'-L'/L-M/A-K/E-J'/H'-H/J-B1/B1 | A/M-L/L'-M'/A'-B2/B2-J/H-H'/J'-E/K (AK,A'B2JB1,EJ',HH'|LM,L'M')
6b: A'/M'-L/L-M/A-K/E-J'/H'-H/J-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-J/H-H'/J'-E/K (AK,A'B2JB1,EJ',HH'|LML'M')
6c: A'/M'-L'/L-M/A-K/E-J'/H'-H'/J'-B1/B1 | A/M-L/L'-M'/A'-B2/B2-J/H-H/J-E/K (AK,A'B2JEJ'B1,H,H'|LM,L'M')
6d: A'/M'-L/L-M/A-K/E-J'/H'-H'/J'-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-J/H-H/J-E/K (AK,A'B2JEJ'B1,H,H'|LML'M')
6e: A/M-L/L-M/A-K/E-J'/H'-H/J-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-J/H-H'/J'-E/K (AKA'B2JB1,EJ',HH'|LM,L'M')
6f: A/M-L'/L-M/A-K/E-J'/H'-H/J-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-J/H-H'/J'-E/K (AKA'B2JB1,EJ',HH'|LML'M')
6g: A/M-L/L-M/A-K/E-J'/H'-H'/J'-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-J/H-H/J-E/K (AKA'B2JEJ'B1,H,H'|LM,L'M')
6h: A/M-L'/L-M/A-K/E-J'/H'-H'/J'-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-J/H-H/J-E/K (AKA'B2JEJ'B1,H,H'|LML'M')

Solution 7: A/M-L/L-M/A-K/E-J/H-H/J-E/K (AK,EJ,H|LM)

Solution 8: A/M-L/L-M/A-K/E-J/H-D2/I2-D1/I1 | A/M-L/L-M/A-I2/D2-I1/D1-H/J-E/K
8a: A'/M'-L'/L-M/A-K/E-J/H-D2/I2-D1/I1 | A/M-L/L'-M'/A'-I2/D2-I1/D1-H/J-E/K (AK,A'I2D1HD2I1,EJ|LM,L'M')
8b: A'/M'-L/L-M/A-K/E-J/H-D2/I2-D1/I1 | A/M-L'/L'-M'/A'-I2/D2-I1/D1-H/J-E/K (AK,A'I2D1HD2I1,EJ|LML'M')
8c: A/M-L/L-M/A-K/E-J/H-D2/I2-D1/I1 | A'/M'-L'/L'-M'/A'-I2/D2-I1/D1-H/J-E/K (AKA'I2D1HD2I1,EJ|LM,L'M')
8d: A/M-L'/L-M/A-K/E-J/H-D2/I2-D1/I1 | A'/M'-L/L'-M'/A'-I2/D2-I1/D1-H/J-E/K (AKA'I2D1HD2I1,EJ|LML'M')

Solution 9: A/M-L/L-M/A-K/E-G2/G2-F1/C1-C1/F1 | A/M-L/L-M/A-F2/C2-C2/F2-G1/G1-E/K
9a: A'/M'-L'/L-M/A-K/E-G2/G2-F1/C1-C1/F1 | A/M-L/L'-M'/A'-F2/C2-C2/F2-G1/G1-E/K (AK,A'F2G1EG2F1,C1,C2|LM,L'M')
9b: A'/M'-L/L-M/A-K/E-G2/G2-F1/C1-C1/F1 | A/M-L'/L'-M'/A'-F2/C2-C2/F2-G1/G1-E/K (AK,A'F2G1EG2F1,C1,C2|LML'M')
9c: A/M-L/L-M/A-K/E-G2/G2-F1/C1-C1/F1 | A'/M'-L'/L'-M'/A'-F2/C2-C2/F2-G1/G1-E/K (AKA'F2G1EG2F1,C1,C2|LM,L'M')
9d: A/M-L'/L-M/A-K/E-G2/G2-F1/C1-C1/F1 | A'/M'-L/L'-M'/A'-F2/C2-C2/F2-G1/G1-E/K (AKA'F2G1EG2F1,C1,C2|LML'M')

Solution 10: A/M-L/L-M/A-K/E-G2/G2-G1/G1-B1/B1 | A/M-L/L-M/A-B2/B2-G2/G2-G1/G1-E/K
10a: A'/M'-L'/L-M/A-K/E-G2'/G2'-G1'/G1'-B1/B1 | A/M-L/L'-M'/A'-B2/B2-G2/G2-G1/G1-E/K (AK,A'B2G2G1EG2'G1'B1|LM,L'M')
10b: A'/M'-L/L-M/A-K/E-G2'/G2'-G1'/G1'-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-G2/G2-G1/G1-E/K (AK,A'B2G2G1EG2'G1'B1|LML'M')
10c: A'/M'-L'/L-M/A-K/E-G2'/G2-G1/G1'-B1/B1 | A/M-L/L'-M'/A'-B2/B2-G2/G2'-G1'/G1-E/K (AK,A'B2G2G1EG2'G1'B1|LM,L'M')
10d: A'/M'-L/L-M/A-K/E-G2'/G2-G1/G1'-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-G2/G2'-G1'/G1-E/K (AK,A'B2G2G1EG2'G1'B1|LML'M')
10e: A/M-L/L-M/A-K/E-G2'/G2'-G1'/G1'-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-G2/G2-G1/G1-E/K (AKA'B2G2G1EG2'G1'B1|LM,L'M')
10f: A/M-L'/L-M/A-K/E-G2'/G2'-G1'/G1'-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-G2/G2-G1/G1-E/K (AKA'B2G2G1EG2'G1'B1|LML'M')
10g: A/M-L/L-M/A-K/E-G2'/G2-G1/G1'-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-G2/G2'-G1'/G1-E/K (AKA'B2G2G1EG2'G1'B1|LM,L'M')
10h: A/M-L'/L-M/A-K/E-G2'/G2-G1/G1'-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-G2/G2'-G1'/G1-E/K (AKA'B2G2G1EG2'G1'B1|LML'M')

Solution 11: A/M-L/L-M/A-K/E-G2/G2-G1/G1-E/K (AK,EG2G1|LM)

Solution 12: A/M-L/L-M/A-K/E-G2/G2-H/J-B1/B1 | A/M-L/L-M/A-B2/B2-J/H-G1/G1-E/K
12a: A'/M'-L'/L-M/A-K/E-G2/G2-H/J-B1/B1 | A/M-L/L'-M'/A'-B2/B2-J/H-G1/G1-E/K (AK,A'B2JB1,EG2HG1|LM,L'M')
12b: A'/M'-L/L-M/A-K/E-G2/G2-H/J-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-J/H-G1/G1-E/K (AK,A'B2JB1,EG2HG1|LML'M')
12c: A/M-L/L-M/A-K/E-G2/G2-H/J-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-J/H-G1/G1-E/K (AKA'B2JB1,EG2HG1|LM,L'M')
12d: A/M-L'/L-M/A-K/E-G2/G2-H/J-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-J/H-G1/G1-E/K (AKA'B2JB1,EG2HG1|LML'M')

Solution 13: A/M-L/L-M/A-K/E-G2/G2-D2/I2-D1/I1 | A/M-L/L-M/A-I2/D2-I1/D1-G1/G1-E/K
13a: A'/M'-L'/L-M/A-K/E-G2/G2-D2/I2-D1/I1 | A/M-L/L'-M'/A'-I2/D2-I1/D1-G1/G1-E/K (AK,A'I2D1G1EG2D2I1|LM,L'M')
13b: A'/M'-L/L-M/A-K/E-G2/G2-D2/I2-D1/I1 | A/M-L'/L'-M'/A'-I2/D2-I1/D1-G1/G1-E/K (AK,A'I2D1G1EG2D2I1|LML'M')
13c: A/M-L/L-M/A-K/E-G2/G2-D2/I2-D1/I1 | A'/M'-L'/L'-M'/A'-I2/D2-I1/D1-G1/G1-E/K (AKA'I2D1G1EG2D2I1|LM,L'M')
13d: A/M-L'/L-M/A-K/E-G2/G2-D2/I2-D1/I1 | A'/M'-L/L'-M'/A'-I2/D2-I1/D1-G1/G1-E/K (AKA'I2D1G1EG2D2I1|LML'M')

Solution 14: A/M-L/L-M/A-K/E-C2/F2-G1/G1-C1/F1 | A/M-L/L-M/A-F2/C2-G2/G2-F1/C1-E/K
14a: A'/M'-L'/L-M/A-K/E-C2/F2-G1/G1-C1/F1 | A/M-L/L'-M'/A'-F2/C2-G2/G2-F1/C1-E/K (AK,A'F2G1C1EC2G2F1|LM,L'M')
14b: A'/M'-L/L-M/A-K/E-C2/F2-G1/G1-C1/F1 | A/M-L'/L'-M'/A'-F2/C2-G2/G2-F1/C1-E/K (AK,A'F2G1C1EC2G2F1|LML'M')
14c: A/M-L/L-M/A-K/E-C2/F2-G1/G1-C1/F1 | A'/M'-L'/L'-M'/A'-F2/C2-G2/G2-F1/C1-E/K (AKA'F2G1C1EC2G2F1|LM,L'M')
14d: A/M-L'/L-M/A-K/E-C2/F2-G1/G1-C1/F1 | A'/M'-L/L'-M'/A'-F2/C2-G2/G2-F1/C1-E/K (AKA'F2G1C1EC2G2F1|LML'M')

Solution 15: A/M-L/L-M/A-K/E-C2/F2-H/J-C1/F1 | A/M-L/L-M/A-F2/C2-J/H-F1/C1-E/K
15a: A'/M'-L'/L-M/A-K/E-C2/F2-H/J-C1/F1 | A/M-L/L'-M'/A'-F2/C2-J/H-F1/C1-E/K (AK,A'F2HF1,C1EC2J|LM,L'M')
15b: A'/M'-L/L-M/A-K/E-C2/F2-H/J-C1/F1 | A/M-L'/L'-M'/A'-F2/C2-J/H-F1/C1-E/K (AK,A'F2HF1,C1EC2J|LML'M')
15c: A/M-L/L-M/A-K/E-C2/F2-H/J-C1/F1 | A'/M'-L'/L'-M'/A'-F2/C2-J/H-F1/C1-E/K (AKA'F2HF1,C1EC2J|LM,L'M')
15d: A/M-L'/L-M/A-K/E-C2/F2-H/J-C1/F1 | A'/M'-L/L'-M'/A'-F2/C2-J/H-F1/C1-E/K (AKA'F2HF1,C1EC2J|LML'M')

Solution 16: A/M-L/L-M/A-I2/D2-I1/D1-F1/C1-C1/F1 | A/M-L/L-M/A-F2/C2-C2/F2-D2/I2-D1/I1
16a: A'/M'-L'/L-M/A-I2/D2-I1/D1-F1/C1-C1/F1 | A/M-L/L'-M'/A'-F2/C2-C2/F2-D2/I2-D1/I1 (AI2D1F1A'F2D2I1,C1,C2|LM,L'M')
16b: A'/M'-L/L-M/A-I2/D2-I1/D1-F1/C1-C1/F1 | A/M-L'/L'-M'/A'-F2/C2-C2/F2-D2/I2-D1/I1 (AI2D1F1A'F2D2I1,C1,C2|LML'M')
16c: A/M-L/L-M/A-I2/D2-I1/D1-F1/C1-C1/F1 | A'/M'-L'/L'-M'/A'-F2/C2-C2/F2-D2/I2-D1/I1 (AI2D1F1,A'F2D2I1,C1,C2|LM,L'M')
16d: A/M-L'/L-M/A-I2/D2-I1/D1-F1/C1-C1/F1 | A'/M'-L/L'-M'/A'-F2/C2-C2/F2-D2/I2-D1/I1 (AI2D1F1,A'F2D2I1,C1,C2|LML'M')

Solution 17: A/M-L/L-M/A-I2/D2-I1/D1-G1/G1-B1/B1 | A/M-L/L-M/A-B2/B2-G2/G2-D2/I2-D1/I1
17a: A'/M'-L'/L-M/A-I2/D2-I1/D1-G1/G1-B1/B1 | A/M-L/L'-M'/A'-B2/B2-G2/G2-D2/I2-D1/I1 (AI2D1G1B1A'B2G2D2I1|LM,L'M')
17b: A'/M'-L/L-M/A-I2/D2-I1/D1-G1/G1-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-G2/G2-D2/I2-D1/I1 (AI2D1G1B1A'B2G2D2I1|LML'M')
17c: A/M-L/L-M/A-I2/D2-I1/D1-G1/G1-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-G2/G2-D2/I2-D1/I1 (AI2D1G1B1,A'B2G2D2I1|LM,L'M')
17d: A/M-L'/L-M/A-I2/D2-I1/D1-G1/G1-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-G2/G2-D2/I2-D1/I1 (AI2D1G1B1,A'B2G2D2I1|LML'M')

Solution 18: A/M-L/L-M/A-I2/D2-I1/D1-H/J-B1/B1 | A/M-L/L-M/A-B2/B2-J/H-D2/I2-D1/I1
18a: A'/M'-L'/L-M/A-I2/D2-I1/D1-H/J-B1/B1 | A/M-L/L-M'/A'-B2/B2-J/H-D2/I2-D1/I1 (AI2D1HD2I1,A'B2JB1|LM,L'M')
18b: A'/M'-L/L-M/A-I2/D2-I1/D1-H/J-B1/B1 | A/M-L'/L-M'/A'-B2/B2-J/H-D2/I2-D1/I1 (AI2D1HD2I1,A'B2JB1|LML'M')
18c: A/M-L/L-M/A-I2/D2-I1/D1-H/J-B1/B1 | A'/M'-L'/L-M'/A'-B2/B2-J/H-D2/I2-D1/I1 (AI2D1HD2I1A'B2JB1|LM,L'M')
18d: A/M-L'/L-M/A-I2/D2-I1/D1-H/J-B1/B1 | A'/M'-L/L-M'/A'-B2/B2-J/H-D2/I2-D1/I1 (AI2D1HD2I1A'B2JB1|LML'M')

Solution 19: A/M-L/L-M/A-I2/D2-I1/D1-D2/I2-D1/I1 (AI2D1D2I1|LM)

Solution 20: A/M-L/L-M/A-I2/D2-J/H-D2/I2-B1/B1 | A/M-L/L-M/A-B2/B2-I1/D1-H/J-D1/I1
20a: A'/M'-L'/L-M/A-I2/D2-J/H-D2/I2-B1/B1 | A/M-L/L'-M'/A'-B2/B2-I1/D1-H/J-D1/I1 (AI2B1A'B2I1,D1HD2J|LM,L'M')
20b: A'/M'-L/L-M/A-I2/D2-J/H-D2/I2-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-I1/D1-H/J-D1/I1 (AI2B1A'B2I1,D1HD2J|LML'M')
20c: A/M-L/L-M/A-I2/D2-J/H-D2/I2-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-I1/D1-H/J-D1/I1 (AI2B1,A'B2I1,D1HD2J|LM,L'M')
20d: A/M-L'/L-M/A-I2/D2-J/H-D2/I2-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-I1/D1-H/J-D1/I1 (AI2B1,A'B2I1,D1HD2J|LML'M')

Solution 21: A/M-L/L-M/A-I2/D2-G2/G2-D2/I2-B1/B1 | A/M-L/L-M/A-B2/B2-I1/D1-G1/G1-D1/I1
21a: A'/M'-L'/L-M/A-I2/D2-G2/G2-D2/I2-B1/B1 | A/M-L/L'-M'/A'-B2/B2-I1/D1-G1/G1-D1/I1 (AI2B1A'B2I1,D1G1,D2G2|LM,L'M')
21b: A'/M'-L/L-M/A-I2/D2-G2/G2-D2/I2-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-I1/D1-G1/G1-D1/I1 (AI2B1A'B2I1,D1G1,D2G2|LML'M')
21c: A/M-L/L-M/A-I2/D2-G2/G2-D2/I2-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-I1/D1-G1/G1-D1/I1 (AI2B1,A'B2I1,D1G1,D2G2|LM,L'M')
21d: A/M-L'/L-M/A-I2/D2-G2/G2-D2/I2-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-I1/D1-G1/G1-D1/I1 (AI2B1,A'B2I1,D1G1,D2G2|LML'M')

Solution 22: A/M-L/L-M/A-I2/D2-C2/F2-D2/I2-C1/F1 | A/M-L/L-M/A-F2/C2-I1/D1-F1/C1-D1/I1
22a: A'/M'-L'/L-M/A-I2/D2-C2/F2-D2/I2-C1/F1 | A/M-L/L'-M'/A'-F2/C2-I1/D1-F1/C1-D1/I1 (AI2C1D1F1A'F2D2C2I1|LM,L'M')
22b: A'/M'-L/L-M/A-I2/D2-C2/F2-D2/I2-C1/F1 | A/M-L'/L'-M'/A'-F2/C2-I1/D1-F1/C1-D1/I1 (AI2C1D1F1A'F2D2C2I1|LML'M')
22c: A/M-L/L-M/A-I2/D2-C2/F2-D2/I2-C1/F1 | A'/M'-L'/L'-M'/A'-F2/C2-I1/D1-F1/C1-D1/I1 (AI2C1D1F1,A'F2D2C2I1|LM,L'M')
22d: A/M-L'/L-M/A-I2/D2-C2/F2-D2/I2-C1/F1 | A'/M'-L/L'-M'/A'-F2/C2-I1/D1-F1/C1-D1/I1 (AI2C1D1F1,A'F2D2C2I1|LML'M')

Solution 23: A/M-L/L-M/A-F2/C2-J/H-F1/C1-B1/B1 | A/M-L/L-M/A-B2/B2-C2/F2-H/J-C1/F1
23a: A'/M'-L'/L-M/A-F2/C2-J/H-F1/C1-B1/B1 | A/M-L/L'-M'/A'-B2/B2-C2/F2-H/J-C1/F1 (AF2HF1,A'B2C2JC1B1|LM,L'M')
23b: A'/M'-L/L-M/A-F2/C2-J/H-F1/C1-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-C2/F2-H/J-C1/F1 (AF2HF1,A'B2C2JC1B1|LML'M')
23c: A/M-L/L-M/A-F2/C2-J/H-F1/C1-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-C2/F2-H/J-C1/F1 (AF2HF1A'B2C2JC1B1|LM,L'M')
23d: A/M-L'/L-M/A-F2/C2-J/H-F1/C1-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-C2/F2-H/J-C1/F1 (AF2HF1A'B2C2JC1B1|LML'M')

Solution 24: A/M-L/L-M/A-F2/C2-G2/G2-F1/C1-B1/B1 | A/M-L/L-M/A-B2/B2-C2/F2-G1/G1-C1/F1
24a: A'/M'-L'/L-M/A-F2/C2-G2/G2-F1/C1-B1/B1 | A/M-L/L'-M'/A'-B2/B2-C2/F2-G1/G1-C1/F1 (AF2G1C1B1A'B2C2G2F1|LM,L'M')
24b: A'/M'-L/L-M/A-F2/C2-G2/G2-F1/C1-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-C2/F2-G1/G1-C1/F1 (AF2G1C1B1A'B2C2G2F1|LML'M')
24c: A/M-L/L-M/A-F2/C2-G2/G2-F1/C1-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-C2/F2-G1/G1-C1/F1 (AF2G1C1B1,A'B2C2G2F1|LM,L'M')
24d: A/M-L'/L-M/A-F2/C2-G2/G2-F1/C1-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-C2/F2-G1/G1-C1/F1 (AF2G1C1B1,A'B2C2G2F1|LML'M')

Solution 25: A/M-L/L-M/A-F2/C2-C2/F2-F1/C1-C1/F1 (AF2F1,C1,C2|LM)

Solution 26: A/M-L/L-M/A-F2/C2-C2/F2-G1/G1-B1/B1 | A/M-L/L-M/A-B2/B2-G2/G2-F1/C1-C1/F1
26a: A'/M'-L'/L-M/A-F2/C2-C2/F2-G1/G1-B1/B1 | A/M-L/L'-M'/A'-B2/B2-G2/G2-F1/C1-C1/F1 (AF2G1B1A'B2G2F1,C1,C2|LM,L'M')
26b: A'/M'-L/L-M/A-F2/C2-C2/F2-G1/G1-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-G2/G2-F1/C1-C1/F1 (AF2G1B1A'B2G2F1,C1,C2|LML'M')
26c: A/M-L/L-M/A-F2/C2-C2/F2-G1/G1-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-G2/G2-F1/C1-C1/F1 (AF2G1B1,A'B2G2F1,C1,C2|LM,L'M')
26d: A/M-L'/L-M/A-F2/C2-C2/F2-G1/G1-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-G2/G2-F1/C1-C1/F1 (AF2G1B1,A'B2G2F1,C1,C2|LML'M')

Solution 27: A/M-L/L-M/A-F2/C2-C2/F2-H/J-B1/B1 | A/M-L/L-M/A-B2/B2-J/H-F1/C1-C1/F1
27a: A'/M'-L'/L-M/A-F2/C2-C2/F2-H/J-B1/B1 | A/M-L/L'-M'/A'-B2/B2-J/H-F1/C1-C1/F1 (AF2HF1,A'B2JB1,C1,C2|LM,L'M')
27b: A'/M'-L/L-M/A-F2/C2-C2/F2-H/J-B1/B1 | A/M-L'/L'-M'/A'-B2/B2-J/H-F1/C1-C1/F1 (AF2HF1,A'B2JB1,C1,C2|LML'M')
27c: A/M-L/L-M/A-F2/C2-C2/F2-H/J-B1/B1 | A'/M'-L'/L'-M'/A'-B2/B2-J/H-F1/C1-C1/F1 (AF2HF1A'B2JB1,C1,C2|LM,L'M')
27d: A/M-L'/L-M/A-F2/C2-C2/F2-H/J-B1/B1 | A'/M'-L/L'-M'/A'-B2/B2-J/H-F1/C1-C1/F1 (AF2HF1A'B2JB1,C1,C2|LML'M')

Solution 28: A/M-L/L-M/A-B2/B2-J/H-G1/G1-B1/B1 | A/M-L/L-M/A-B2/B2-G2/G2-H/J-B1/B1
28a: A'/M'-L'/L-M/A-B2/B2-J/H-G1/G1-B1'/B1' | A/M-L/L'-M'/A'-B2'/B2'-G2/G2-H/J-B1/B1 (AB2JB1,A'B2'G2HG1B1'|LM,L'M')
28b: A'/M'-L/L-M/A-B2/B2-J/H-G1/G1-B1'/B1' | A/M-L'/L'-M'/A'-B2'/B2'-G2/G2-H/J-B1/B1 (AB2JB1,A'B2'G2HG1B1'|LML'M')
28c: A'/M'-L'/L-M/A-B2/B2'-J/H-G1/G1-B1/B1' | A/M-L/L'-M'/A'-B2'/B2-G2/G2-H/J-B1'/B1 (AB2G2HG1B1,A'B2'JB1'|LM,L'M')
28d: A'/M'-L/L-M/A-B2/B2'-J/H-G1/G1-B1/B1' | A/M-L'/L'-M'/A'-B2'/B2-G2/G2-H/J-B1'/B1 (AB2G2HG1B1,A'B2'JB1'|LML'M')
28e: A/M-L/L-M/A-B2/B2-J/H-G1/G1-B1'/B1' | A'/M'-L'/L'-M'/A'-B2'/B2'-G2/G2-H/J-B1/B1 (AB2JB1A'B2'G2HG1B1'|LM,L'M')
28f: A/M-L'/L-M/A-B2/B2-J/H-G1/G1-B1'/B1' | A'/M'-L/L'-M'/A'-B2'/B2'-G2/G2-H/J-B1/B1 (AB2JB1A'B2'G2HG1B1'|LML'M')
28g: A/M-L/L-M/A-B2/B2'-J/H-G1/G1-B1/B1' | A'/M'-L'/L'-M'/A'-B2'/B2-G2/G2-H/J-B1'/B1 (AB2G2HG1B1A'B2'JB1'|LM,L'M')
28h: A/M-L'/L-M/A-B2/B2'-J/H-G1/G1-B1/B1' | A'/M'-L/L'-M'/A'-B2'/B2-G2/G2-H/J-B1'/B1 (AB2G2HG1B1A'B2'JB1'|LML'M')

Solution 29: A/M-L/L-M/A-B2/B2-J/H-H/J-B1/B1 (AB2JB1,H|LM)

Solution 30: A/M-L/L-M/A-B2/B2-G2/G2-G1/G1-B1/B1 (AB2G2G1B1|LM)

2|a, 2|b: 7

3|a, 2|b: 25

4|a, 2|b: 1a, 2a, 3a, 5a, 5g, 6a, 12a, 15a, 16c, 26c, 27a, 29
4|a, 4|b: 1b, 2b, 3b, 5b, 5h, 6b, 12b, 15b, 16d, 26d, 27b

5|a, 2|b: 17c, 19, 22c, 24c, 30
5|a, 4|b: 17d, 22d, 24d

6|a, 2|b: 1c, 3c, 4a, 5e, 6c, 6e, 8a, 9a, 11, 21a, 21c
6|a, 4|b: 1d, 3d, 4b, 5f, 6d, 6f, 8b, 9b, 21b, 21d

8|a, 2|b: 4c, 6g, 8c, 9c, 10a, 10c, 13a, 14a, 16a, 26a, 27c
8|a, 4|b: 4d, 6h, 8d, 9d, 10b, 10d, 13b, 14b, 16b, 26b, 27d

10|a, 2|b: 10e, 10g, 13c, 14c, 17a, 18c, 22a, 23c, 24a, 28e, 28g
10|a, 4|b: 10f, 10h, 13d, 14d, 17b, 18d, 22b, 23d, 24b, 28f, 28h

12|a, 2|b: 2c, 5c, 12c, 15c, 18a, 20a, 20c, 23a, 28a, 28c
12|a, 4|b: 2d, 5d, 12d, 15d, 18b, 20b, 20d, 23b, 28b, 28d
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Tue Apr 07, 2015 7:43 am

Type AAAABAB:

Edge data:
Code: Select all
b a b a a
a       a
a a A b a : A1 xJ1 -H,A2

b a b a b
a       a
a a A a a : B xL -I,F2,C2

a b a a a
b       b
a a A b a : C1 xC1 -A1,B

a b a a b
b       a
a a A a b : D1 xF1 -C1,D1,E

a b a b a
b       b
a a A a a : E xI -F1,G,D2

b a a a a
a       b
b a A b a : F1 xD1 -A1,B

b a a a b
a       a
b a A a b : G xG -C1,D1,E

b a a b a
a       b
b a A a a : D2 xF2 -F1,G,D2

a a b a a
a       a
a b A b a : H xK -H,A2

a a b a b
a       a
a b A a a : A2 xJ2 -I,F2,C2

a a a a a
b       b
a b A b a : I xE -A1,B

a a a a b
b       a
a b A a b : F2 xD2 -C1,D1,E

a a a b a
b       b
a b A a a : C2 xC2 -F1,G,D2

a b a a a
a       a
a a B a b : J1 xA1 -J1,K

a b a b a
a       a
a a B a a : K xH -L,J2

a a a a a
a       a
b a B a b : L xB -J1,K

a a a b a
a       a
b a B a a : J2 xA2 -L,J2


Vertex sequence:
A1/J1 B/L
J1/A1 K/H
H/K A2/J2
L/B J2/A2
I/E F2/D2 C2/C2
F1/D1 G/G D2/F2
C1/C1 D1/F1 E/I

432 possible sequences, leading to 38 basic solutions:

Solution 1: A1/J1-J1/A1-H/K-L/B-I/E-F1/D1-D1/F1 | B/L-K/H-A2/J2-J2/A2-F2/D2-D2/F2-E/I (A1HA2F2EF1,BI,D1,D2|J1,KL,J2)

Solution 2: A1/J1-J1/A1-H/K-L/B-I/E-G/G-C1/C1 | B/L-K/H-A2/J2-J2/A2-C2/C2-G/G-E/I
2a: A1/J1-J1/A1-H/K-L/B-I/E-G'/G-C1/C1 | B/L-K/H-A2/J2-J2/A2-C2/C2-G/G'-E/I (A1HA2C2GC1,BI,EG'|J1,KL,J2)
2a: A1/J1-J1/A1-H/K-L/B-I/E-G'/G'-C1/C1 | B/L-K/H-A2/J2-J2/A2-C2/C2-G/G-E/I (A1HA2C2GEG'C1,BI|J1,KL,J2)

Solution 3: A1/J1-J1/A1-H/K-L/B-I/E-G/G-E/I | B/L-K/H-A2/J2-J2/A2-I/E-G/G-E/I
3a: A1/J1-J1/A1-H/K-L/B-I'/E'-G'/G-E/I | B/L-K/H-A2/J2-J2/A2-I/E-G/G'-E'/I' (A1HA2I,BI',EG,E'G'|J1,KL,J2)
3b: A1/J1-J1/A1-H/K-L/B-I'/E'-G'/G'-E/I | B/L-K/H-A2/J2-J2/A2-I/E-G/G-E'/I' (A1HA2I,BI',EGE'G'|J1,KL,J2)
3c: A1/J1-J1/A1-H/K-L/B-I'/E'-G'/G'-E'/I' | B/L-K/H-A2/J2-J2/A2-I/E-G/G-E/I (A1HA2IBI',EG,E'G'|J1,KL,J2)
3d: A1/J1-J1/A1-H/K-L/B-I'/E'-G'/G-E'/I' | B/L-K/H-A2/J2-J2/A2-I/E-G/G'-E/I (A1HA2IBI',EGE'G'|J1,KL,J2)

Solution 4: A1/J1-J1/A1-H/K-L/B-I/E-D2/F2-D1/F1 | B/L-K/H-A2/J2-J2/A2-F2/D2-F1/D1-E/I (A1HA2F2D1ED2F1,BI|J1,KL,J2)

Solution 5: A1/J1-J1/A1-H/K-L/B-F2/D2-F1/D1-C1/C1 | B/L-K/H-A2/J2-J2/A2-C2/C2-D2/F2-D1/F1 (A1HA2C2D2F1BF2D1C1|J1,KL,J2)

Solution 6: A1/J1-J1/A1-H/K-L/B-F2/D2-F1/D1-E/I | B/L-K/H-A2/J2-J2/A2-I/E-D2/F2-D1/F1 (A1HA2I,BF2D1ED2F1|J1,KL,J2)

Solution 7: A1/J1-J1/A1-H/K-L/B-F2/D2-D2/F2-C1/C1 | B/L-K/H-A2/J2-J2/A2-C2/C2-F1/D1-D1/F1 (A1HA2C2F1BF2C1,D1,D2|J1,KL,J2)

Solution 8: A1/J1-J1/A1-H/K-L/B-F2/D2-D2/F2-E/I | B/L-K/H-A2/J2-J2/A2-I/E-F1/D1-D1/F1 (A1HA2I,BF2EF1,D1,D2|J1,KL,J2)

Solution 9: A1/J1-J1/A1-H/K-L/B-C2/C2-F1/D1-D1/F1 | B/L-K/H-A2/J2-J2/A2-F2/D2-D2/F2-C1/C1 (A1HA2F2C1BC2F1,D1,D2|J1,KL,J2)

Solution 10: A1/J1-J1/A1-H/K-L/B-C2/C2-G/G-C1/C1 | B/L-K/H-A2/J2-J2/A2-C2/C2-G/G-C1/C1
10a: A1/J1-J1/A1-H/K-L/B-C2'/C2'-G'/G'-C1'/C1' | B/L-K/H-A2/J2-J2/A2-C2/C2-G/G-C1/C1 (A1HA2C2GC1BC2'G'C1'|J1,KL,J2)
10b: A1/J1-J1/A1-H/K-L/B-C2'/C2'-G'/G-C1/C1 | B/L-K/H-A2/J2-J2/A2-C2/C2-G/G'-C1'/C1' (A1HA2C2GC1,BC2'G'C1'|J1,KL,J2)
10c: A1/J1-J1/A1-H/K-L/B-C2'/C2-G/G-C1/C1' | B/L-K/H-A2/J2-J2/A2-C2/C2'-G'/G'-C1'/C1 (A1HA2C2GC1BC2'G'C1'|J1,KL,J2)
10d: A1/J1-J1/A1-H/K-L/B-C2'/C2-G/G'-C1'/C1 | B/L-K/H-A2/J2-J2/A2-C2/C2'-G'/G-C1/C1' (A1HA2C2GC1,BC2'G'C1'|J1,KL,J2)

Solution 11: A1/J1-J1/A1-H/K-L/B-C2/C2-G/G-E/I | B/L-K/H-A2/J2-J2/A2-I/E-G/G-C1/C1
11a: A1/J1-J1/A1-H/K-L/B-C2/C2-G/G'-E/I | B/L-K/H-A2/J2-J2/A2-I/E-G'/G-C1/C1 (A1HA2I,BC2GC1,EG'|J1,KL,J2)
11b: A1/J1-J1/A1-H/K-L/B-C2/C2-G/G-E/I | B/L-K/H-A2/J2-J2/A2-I/E-G'/G'-C1/C1 (A1HA2I,BC2GEG'C1|J1,KL,J2)

Solution 12: A1/J1-J1/A1-H/K-L/B-C2/C2-D2/F2-D1/F1 | B/L-K/H-A2/J2-J2/A2-F2/D2-F1/D1-C1/C1 (A1HA2F2D1C1BC2D2F1|J1,KL,J2)

Solution 13: A1/J1-J1/A1-A2/J2-J2/A2-I/E-F1/D1-D1/F1 | A1/J1-J1/A1-A2/J2-J2/A2-F2/D2-D2/F2-E/I
13a: A1'/J1'-J1/A1-A2/J2-J2'/A2'-I/E-F1/D1-D1/F1 | A1/J1-J1'/A1'-A2'/J2'-J2/A2-F2/D2-D2/F2-E/I (A1A2F2EF1A1'A2'I,D1,D2|J1J1',J2J2')
13b: A1/J1-J1/A1-A2/J2-J2/A2-I/E-F1/D1-D1/F1 | A1'/J1'-J1'/A1'-A2'/J2'-J2'/A2'-F2/D2-D2/F2-E/I (A1A2IA1'A2'F2EF1,D1,D2|J1,J1',J2,J2')

Solution 14: A1/J1-J1/A1-A2/J2-J2/A2-I/E-G/G-C1/C1 | A1/J1-J1/A1-A2/J2-J2/A2-C2/C2-G/G-E/I
14a: A1'/J1'-J1/A1-A2/J2-J2'/A2'-I/E-G'/G-C1/C1 | A1/J1-J1'/A1'-A2'/J2'-J2/A2-C2/C2-G/G'-E/I (A1A2C2GC1A1'A2'I,EG'|J1J1',J2J2')
14b: A1'/J1'-J1/A1-A2/J2-J2'/A2'-I/E-G'/G'-C1/C1 | A1/J1-J1'/A1'-A2'/J2'-J2/A2-C2/C2-G/G-E/I (A1A2C2GEG'C1A1'A2'I|J1J1',J2J2')
14c: A1/J1-J1/A1-A2/J2-J2/A2-I/E-G'/G-C1/C1 | A1'/J1'-J1'/A1'-A2'/J2'-J2'/A2'-C2/C2-G/G'-E/I (A1A2IA1'A2'C2GC1,EG'|J1,J1',J2,J2')
14d: A1/J1-J1/A1-A2/J2-J2/A2-I/E-G'/G'-C1/C1 | A1'/J1'-J1'/A1'-A2'/J2'-J2'/A2'-C2/C2-G/G-E/I (A1A2IA1'A2'C2GEG'C1|J1,J1',J2,J2')

Solution 15: A1/J1-J1/A1-A2/J2-J2/A2-I/E-G/G-E/I (A1A2I,EG|J1,J2)

Solution 16: A1/J1-J1/A1-A2/J2-J2/A2-I/E-D2/F2-D1/F1 | A1/J1-J1/A1-A2/J2-J2/A2-F2/D2-F1/D1-E/I
16a: A1'/J1'-J1/A1-A2/J2-J2'/A2'-I/E-D2/F2-D1/F1 | A1/J1-J1'/A1'-A2'/J2'-J2/A2-F2/D2-F1/D1-E/I (A1A2F2D1ED2F1A1'A1A2'I|J1J1',J2J2')
16b: A1/J1-J1/A1-A2/J2-J2/A2-I/E-D2/F2-D1/F1 | A1'/J1'-J1'/A1'-A2'/J2'-J2'/A2'-F2/D2-F1/D1-E/I (A1A2IA1'A2'F2D1ED2F1|J1,J1',J2,J2')

Solution 17: A1/J1-J1/A1-A2/J2-J2/A2-F2/D2-F1/D1-C1/C1 | A1/J1-J1/A1-A2/J2-J2/A2-C2/C2-D2/F2-D1/F1
17a: A1'/J1'-J1/A1-A2/J2-J2'/A2'-F2/D2-F1/D1-C1/C1 | A1/J1-J1'/A1'-A2'/J2'-J2/A2-C2/C2-D2/F2-D1/F1 (A1A2C2D2F1,A1'A2'F2D1C1|J1J1',J2J2')
17b: A1/J1-J1/A1-A2/J2-J2/A2-F2/D2-F1/D1-C1/C1 | A1'/J1'-J1'/A1'-A2'/J2'-J2'/A2'-C2/C2-D2/F2-D1/F1 (A1A2F2D1C1,A1'A2'C2D2F1|J1,J1',J2,J2')

Solution 18: A1/J1-J1/A1-A2/J2-J2/A2-F2/D2-D2/F2-C1/C1 | A1/J1-J1/A1-A2/J2-J2/A2-C2/C2-F1/D1-D1/F1
18a: A1'/J1'-J1/A1-A2/J2-J2'/A2'-F2/D2-D2/F2-C1/C1 | A1/J1-J1'/A1'-A2'/J2'-J2/A2-C2/C2-F1/D1-D1/F1 (A1A2C2F1,A1'A2'F2C1,D1,D2|J1J1',J2J2')
18b (chiral): A1/J1-J1/A1-A2/J2-J2/A2-F2/D2-D2/F2-C1/C1 | A1'/J1'-J1'/A1'-A2'/J2'-J2'/A2'-C2/C2-F1/D1-D1/F1 (A1A2F2C1,D2|J1,J2)/(A1'A2'C2F1,D1|J1',J2')

Solution 19: A1/J1-J1/A1-A2/J2-J2/A2-C2/C2-G/G-C1/C1 (A1A2C2GC1|J1,J2)

Solution 20: A1/J1-K/H-A2/J2-L/B-I/E-F1/D1-D1/F1 | B/L-J1/A1-H/K-J2/A2-F2/D2-D2/F2-E/I (A1HA2F2EF1,BI,D1,D2|J1KJ2L)

Solution 21: A1/J1-K/H-A2/J2-L/B-I/E-G/G-C1/C1 | B/L-J1/A1-H/K-J2/A2-C2/C2-G/G-E/I
21a: A1/J1-K/H-A2/J2-L/B-I/E-G'/G-C1/C1 | B/L-J1/A1-H/K-J2/A2-C2/C2-G/G'-E/I (A1HA2C2GC1,BI,EG'|J1KJ2L)
21b: A1/J1-K/H-A2/J2-L/B-I/E-G'/G'-C1/C1 | B/L-J1/A1-H/K-J2/A2-C2/C2-G/G-E/I (A1HA2C2GEG'C1,BI|J1KJ2L)

Solution 22: A1/J1-K/H-A2/J2-L/B-I/E-G/G-E/I | B/L-J1/A1-H/K-J2/A2-I/E-G/G-E/I
22a: A1/J1-K/H-A2/J2-L/B-I'/E'-G'/G-E/I | B/L-J1/A1-H/K-J2/A2-I/E-G/G'-E'/I' (A1HA2I,BI',EG,E'G'|J1KJ2L)
22b: A1/J1-K/H-A2/J2-L/B-I'/E'-G'/G'-E/I | B/L-J1/A1-H/K-J2/A2-I/E-G/G-E'/I' (A1HA2I,BI',EGE'G'|J1KJ2L)
22c: A1/J1-K/H-A2/J2-L/B-I'/E'-G'/G'-E'/I' | B/L-J1/A1-H/K-J2/A2-I/E-G/G-E/I (A1HA2IBI',EG,E'G'|J1KJ2L)
22d: A1/J1-K/H-A2/J2-L/B-I'/E'-G'/G-E'/I' | B/L-J1/A1-H/K-J2/A2-I/E-G/G'-E/I (A1HA2IBI',EGE'G'|J1KJ2L)

Solution 23: A1/J1-K/H-A2/J2-L/B-I/E-D2/F2-D1/F1 | B/L-J1/A1-H/K-J2/A2-F2/D2-F1/D1-E/I (A1HA2F2D1ED2F1,BI|J1KJ2L)

Solution 24: A1/J1-K/H-A2/J2-L/B-F2/D2-F1/D1-C1/C1 | B/L-J1/A1-H/K-J2/A2-C2/C2-D2/F2-D1/F1 (A1HA2C2D2F1BF2D1C1|J1KJ2L)

Solution 25: A1/J1-K/H-A2/J2-L/B-F2/D2-F1/D1-E/I | B/L-J1/A1-H/K-J2/A2-I/E-D2/F2-D1/F1 (A1HA2I,BF2D1ED2F1|J1KJ2L)

Solution 26: A1/J1-K/H-A2/J2-L/B-F2/D2-D2/F2-C1/C1 | B/L-J1/A1-H/K-J2/A2-C2/C2-F1/D1-D1/F1 (A1HA2C2F1BF2C1,D1,D2|J1KJ2L)

Solution 27: A1/J1-K/H-A2/J2-L/B-F2/D2-D2/F2-E/I | B/L-J1/A1-H/K-J2/A2-I/E-F1/D1-D1/F1 (A1HA2I,BF2EF1,D1,D2|J1KJ2L)

Solution 28: A1/J1-K/H-A2/J2-L/B-C2/C2-F1/D1-D1/F1 | B/L-J1/A1-H/K-J2/A2-F2/D2-D2/F2-C1/C1 (A1HA2F2C1BC2F1,D1,D2|J1KJ2L)

Solution 29: A1/J1-K/H-A2/J2-L/B-C2/C2-G/G-C1/C1 | B/L-J1/A1-H/K-J2/A2-C2/C2-G/G-C1/C1
29a: A1/J1-K/H-A2/J2-L/B-C2'/C2'-G'/G'-C1'/C1' | B/L-J1/A1-H/K-J2/A2-C2/C2-G/G-C1/C1 (A1HA2C2GC1BC2'G'C1'|J1KJ2L)
29b: A1/J1-K/H-A2/J2-L/B-C2'/C2'-G'/G-C1/C1' | B/L-J1/A1-H/K-J2/A2-C2/C2-G/G'-C1'/C1 (A1HA2C2GC1BC2'G'C1'|J1KJ2L)
29c: A1/J1-K/H-A2/J2-L/B-C2'/C2-G/G-C1/C1 | B/L-J1/A1-H/K-J2/A2-C2/C2'-G'/G'-C1'/C1' (A1HA2C2GC1,BC2'G'C1'|J1KJ2L)
29d: A1/J1-K/H-A2/J2-L/B-C2'/C2-G/G'-C1'/C1 | B/L-J1/A1-H/K-J2/A2-C2/C2'-G'/G-C1/C1' (A1HA2C2GC1,BC2'G'C1'|J1KJ2L)

Solution 30: A1/J1-K/H-A2/J2-L/B-C2/C2-G/G-E/I | B/L-J1/A1-H/K-J2/A2-I/E-G/G-C1/C1
30a: A1/J1-K/H-A2/J2-L/B-C2/C2-G/G'-E/I | B/L-J1/A1-H/K-J2/A2-I/E-G'/G-C1/C1 (A1HA2I,BC2GC1,EG'|J1KJ2L)
30b: A1/J1-K/H-A2/J2-L/B-C2/C2-G/G-E/I | B/L-J1/A1-H/K-J2/A2-I/E-G'/G'-C1/C1 (A1HA2I,BC2GEG'C1|J1KJ2L)

Solution 31: A1/J1-K/H-A2/J2-L/B-C2/C2-D2/F2-D1/F1 | B/L-J1/A1-H/K-J2/A2-F2/D2-F1/D1-C1/C1 (A1HA2F2D1C1BC2D2F1|J1KJ2L)

Solution 32: B/L-K/H-H/K-L/B-I/E-F1/D1-D1/F1 | B/L-K/H-H/K-L/B-F2/D2-D2/F2-E/I
32a: B'/L'-K/H-H/K-L/B-I/E-F1/D1-D1/F1 | B/L-K'/H'-H'/K'-L'/B'-F2/D2-D2/F2-E/I (BI,B'F2EF1,D1,D2,H,H'|KLK'L')
32b: B'/L'-K/H-H'/K'-L/B-I/E-F1/D1-D1/F1 | B/L-K'/H'-H/K-L'/B'-F2/D2-D2/F2-E/I (BI,B'F2EF1,D1,D2,HH'|KL',LK')
32c: B/L-K/H-H/K-L/B-I/E-F1/D1-D1/F1 | B'/L'-K'/H'-H'/K'-L'/B'-F2/D2-D2/F2-E/I (BIB'F2EF1,D1,D2,H,H'|KL,K'L')
32d: B/L-K/H-H'/K'-L/B-I/E-F1/D1-D1/F1 | B'/L'-K'/H'-H/K-L'/B'-F2/D2-D2/F2-E/I (BIB'F2EF1,D1,D2,HH'|KL'K'L)

Solution 33: B/L-K/H-H/K-L/B-I/E-G/G-C1/C1 | B/L-K/H-H/K-L/B-C2/C2-G/G-E/I
33a: B'/L'-K/H-H/K-L/B-I/E-G'/G-C1/C1 | B/L-K'/H'-H'/K'-L'/B'-C2/C2-G/G'-E/I (BI,B'C2GC1,EG',H,H'|KLK'L')
33b: B'/L'-K/H-H'/K'-L/B-I/E-G'/G-C1/C1 | B/L-K'/H'-H/K-L'/B'-C2/C2-G/G'-E/I (BI,B'C2GC1,EG',HH'|KL',K'L)
33c: B'/L'-K/H-H/K-L/B-I/E-G'/G'-C1/C1 | B/L-K'/H'-H'/K'-L'/B'-C2/C2-G/G-E/I (BI,B'C2GEG'C1,H,H'|KLK'L')
33d: B'/L'-K/H-H'/K'-L/B-I/E-G'/G'-C1/C1 | B/L-K'/H'-H/K-L'/B'-C2/C2-G/G-E/I (BI,B'C2GEG'C1,HH'|KL',K'L)
33e: B/L-K/H-H/K-L/B-I/E-G'/G-C1/C1 | B'/L'-K'/H'-H'/K'-L'/B'-C2/C2-G/G'-E/I (BIB'C2GC1,EG',H,H'|KL,K'L')
33f: B/L-K/H-H'/K'-L/B-I/E-G'/G-C1/C1 | B'/L'-K'/H'-H/K-L'/B'-C2/C2-G/G'-E/I (BIB'C2GC1,EG',HH'|KL'K'L)
33g: B/L-K/H-H/K-L/B-I/E-G'/G'-C1/C1 | B'/L'-K'/H'-H'/K'-L'/B'-C2/C2-G/G-E/I (BIB'C2GEG'C1,H,H'|KL,L'L')
33h: B/L-K/H-H'/K'-L/B-I/E-G'/G'-C1/C1 | B'/L'-K'/H'-H/K-L'/B'-C2/C2-G/G-E/I (BIB'C2GEG'C1,HH'|KL'K'L)

Solution 34: B/L-K/H-H/K-L/B-I/E-G/G-E/I (BI,EG,H|KL)

Solution 35: B/L-K/H-H/K-L/B-I/E-D2/F2-D1/F1 | B/L-K/H-H/K-L/B-F2/D2-F1/D1-E/I
35a: B'/L'-K/H-H/K-L/B-I/E-D2/F2-D1/F1 | B/L-K'/H'-H'/K'-L'/B'-F2/D2-F1/D1-E/I (BI,B'F2D1ED2D1,H,H'|KLK'L')
35b: B'/L'-K/H-H'/K'-L/B-I/E-D2/F2-D1/F1 | B/L-K'/H'-H/K-L'/B'-F2/D2-F1/D1-E/I (BI,B'F2D1ED2D1,HH'|KL',K'L)
35c: B/L-K/H-H/K-L/B-I/E-D2/F2-D1/F1 | B'/L'-K'/H'-H'/K'-L'/B'-F2/D2-F1/D1-E/I (BIB'F2D1ED2D1,H,H'|KL,K'L')
35d: B/L-K/H-H'/K'-L/B-I/E-D2/F2-D1/F1 | B'/L'-K'/H'-H/K-L'/B'-F2/D2-F1/D1-E/I (BIB'F2D1ED2D1,HH'|KL'K'L)

Solution 36: B/L-K/H-H/K-L/B-F2/D2-F1/D1-C1/C1 | B/L-K/H-H/K-L/B-C2/C2-D2/F2-D1/F1
36a: B'/L'-K/H-H/K-L/B-F2/D2-F1/D1-C1/C1 | B/L-K'/H'-H'/K'-L'/B'-C2/C2-D2/F2-D1/F1 (BF2D1C1B'C2D2F1,H,H'|KLK'L')
36b: B'/L'-K/H-H'/K'-L/B-F2/D2-F1/D1-C1/C1 | B/L-K'/H'-H/K-L'/B'-C2/C2-D2/F2-D1/F1 (BF2D1C1B'C2D2F1,HH'|KL',K'L)
36c: B/L-K/H-H/K-L/B-F2/D2-F1/D1-C1/C1 | B'/L'-K'/H'-H'/K'-L'/B'-C2/C2-D2/F2-D1/F1 (BF2D1C1,B'C2D2F1,H,H'|KL,K'L')
36d: B/L-K/H-H'/K'-L/B-F2/D2-F1/D1-C1/C1 | B'/L'-K'/H'-H/K-L'/B'-C2/C2-D2/F2-D1/F1 (BF2D1C1,B'C2D2F1,HH'|KL'K'L)

Solution 37: B/L-K/H-H/K-L/B-F2/D2-D2/F2-C1/C1 | B/L-K/H-H/K-L/B-C2/C2-F1/D1-D1/F1
37a: B'/L'-K/H-H/K-L/B-F2/D2-D2/F2-C1/C1 | B/L-K'/H'-H'/K'-L'/B'-C2/C2-F1/D1-D1/F1 (BF2C1B'C2F1,D1,D2,H,H'|KLK'L')
37b: B'/L'-K/H-H'/K'-L/B-F2/D2-D2/F2-C1/C1 | B/L-K'/H'-H/K-L'/B'-C2/C2-F1/D1-D1/F1 (BF2C1B'C2F1,D1,D2,HH'|KL',K'L)
37c: B/L-K/H-H/K-L/B-F2/D2-D2/F2-C1/C1 | B'/L'-K'/H'-H'/K'-L'/B'-C2/C2-F1/D1-D1/F1 (BF2C1,B'C2F1,D1,D2,H,H'|KL,K'L')
37d: B/L-K/H-H'/K'-L/B-F2/D2-D2/F2-C1/C1 | B'/L'-K'/H'-H/K-L'/B'-C2/C2-F1/D1-D1/F1 (BF2C1,B'C2F1,D1,D2,HH'|KL'K'L)

Solution 38: B/L-K/H-H/K-L/B-C2/C2-G/G-C1/C1 (BC2GC1,H|KL)

2|a, 2|b: 34

3|a, 2|b: 37c

4|a: 18b
4|a, 2|b: 3a, 3b, 8, 11a, 18a, 32b, 33b, 36c, 38
4|a, 4|b: 22a, 22b, 27, 30a, 32a, 33a, 36d

5|a: 17b, 19
5|a, 2|b: 17a

6|a: 15
6|a, 2|b: 1, 2a, 3c, 32c, 33d, 33e, 35b, 37b
6|a, 4|b: 20, 21a, 22c, 32d, 33c, 33f, 35a, 37a, 37d

8|a: 13b, 14c
8|a, 2|b: 2b, 4, 7, 9, 13a, 14a, 33g, 35c, 36b
8|a, 4|b: 21b, 23, 26, 28, 33h, 35d, 36a

10|a: 14d, 16b
10|a, 2|b: 5, 10a, 10c, 12, 14b, 16a
10|a, 4|b: 24, 29a, 29b, 31

12|a, 2|b: 3d, 6, 10b, 10d, 11b
12|a, 4|b: 22d, 25, 29c, 29d, 30b
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Tue Apr 07, 2015 7:44 am

Type AAABAAB:

Edge data:
Code: Select all
a a b a a
b       a
a a A a b : A1 xJ1 -G1,H,E2

a a b a a
b       b
a a A a a : B xL -I,G2,D2

a a b a a
a       a
b a A a b : C xK -G1,H,E2

a a b a a
a       b
b a A a a : A2 xJ2 -I,G2,D2

a b a a b
a       a
b a A b a : D1 xD1 -A1,B

a b a b a
a       a
b a A b a : E1 xG1 -C,A2

a b a b a
a       a
b a A a b : F xI -D1,E1,F

a b a a b
a       a
a b A b a : G1 xE1 -A1,B

a b a b a
a       a
a b A b a : H xH -C,A2

a b a b a
a       a
a b A a b : E2 xG2 -D1,E1,F

b a a a b
a       a
a b A b a : I xF -A1,B

b a a b a
a       a
a b A b a : G2 xE2 -C,A2

b a a b a
a       a
a b A a b : D2 xD2 -D1,E1,F

b a a a a
a       b
a a B a a : J1 xA1 -J1,K

b a a a b
a       a
a a B a a : K xC -L,J2

a a a a a
b       b
a a B a a : L xB -J1,K

a a a a b
b       a
a a B b a : J2 xA2 -L,J2


Vertex sequence:
A1/J1 B/L
J1/A1 K/C
G1/E1 H/H E2/G2
C/K A2/J2
L/B J2/A2
I/F G2/E2 D2/D2
D1/D1 E1/G1 F/I

432 possible sequences, leading to 38 basic solutions:

Solution 1: A1/J1-J1/A1-G1/E1-C/K-L/B-I/F-E1/G1 | B/L-K/C-E2/G2-A2/J2-J2/A2-G2/E2-F/I (A1G1,BI,CE2FE1,A2G2|J1,KL,J2)

Solution 2: A1/J1-J1/A1-G1/E1-C/K-L/B-G2/E2-D1/D1 | B/L-K/C-E2/G2-A2/J2-J2/A2-D2/D2-E1/G1 (A1G1BG2A2D2E1CE2D1|J1,KL,J2)

Solution 3: A1/J1-J1/A1-G1/E1-C/K-L/B-G2/E2-F/I | B/L-K/C-E2/G2-A2/J2-J2/A2-I/F-E1/G1 (A1G1BG2A2I,CE2FE1|J1,KL,J2)

Solution 4: A1/J1-J1/A1-G1/E1-C/K-L/B-D2/D2-E1/G1 | B/L-K/C-E2/G2-A2/J2-J2/A2-G2/E2-D1/D1 (A1G1,BD2E1CE2D1,A2G2|J1,KL,J2)

Solution 5: A1/J1-J1/A1-G1/E1-A2/J2-J2/A2-I/F-E1/G1 | A1/J1-J1/A1-E2/G2-A2/J2-J2/A2-G2/E2-F/I
5a: A1'/J1'-J1/A1-G1/E1-A2/J2-J2'/A2'-I/F-E1/G1 | A1/J1-J1'/A1'-E2/G2-A2'/J2'-J2/A2-G2/E2-F/I (A1G1A1'E2FE1A2G2A2'I|J1J1',J2J2')
5b: A1/J1-J1/A1-G1/E1-A2/J2-J2/A2-I/F-E1/G1 | A1'/J1'-J1'/A1'-E2/G2-A2'/J2'-J2'/A2'-G2/E2-F/I (A1G1,A1'E2FE1A2I,A2'G2|J1,J1',J2,J2')

Solution 6: A1/J1-J1/A1-G1/E1-A2/J2-J2/A2-G2/E2-D1/D1 | A1/J1-J1/A1-E2/G2-A2/J2-J2/A2-D2/D2-E1/G1
6a: A1'/J1'-J1/A1-G1/E1-A2'/J2'-J2/A2-G2/E2-D1/D1 | A1/J1-J1'/A1'-E2/G2-A2/J2-J2'/A2'-D2/D2-E1/G1 (A1G1,A1'E2D1,A2G2,A2'D2E1|J1J1',J2J2')
6a: A1/J1-J1/A1-G1/E1-A2/J2-J2/A2-G2/E2-D1/D1 | A1'/J1'-J1'/A1'-E2/G2-A2'/J2'-J2'/A2'-D2/D2-E1/G1 (A1G1A1'E2D1,A2G2A2'D2E1|J1,J1',J2,J2')

Solution 7: A1/J1-J1/A1-G1/E1-A2/J2-J2/A2-G2/E2-F/I | A1/J1-J1/A1-E2/G2-A2/J2-J2/A2-I/F-E1/G1
7a: A1'/J1'-J1/A1-G1/E1-A2/J2-J2'/A2'-G2/E2-F/I | A1/J1-J1'/A1'-E2/G2-A2'/J2'-J2/A2-I/F-E1/G1 (A1G1,A1'E2FE1A2I,A2'G2|J1J1',J2J2')
7a: A1/J1-J1/A1-G1/E1-A2/J2-J2/A2-G2/E2-F/I | A1'/J1'-J1'/A1'-E2/G2-A2'/J2'-J2'/A2'-I/F-E1/G1 (A1G1A1'E2FE1A2G2A2'I|J1,J1',J2,J2')

Solution 8: A1/J1-J1/A1-G1/E1-A2/J2-J2/A2-D2/D2-E1/G1 | A1/J1-J1/A1-E2/G2-A2/J2-J2/A2-G2/E2-D1/D1
8a: A1'/J1'-J1/A1-G1/E1-A2'/J2'-J2/A2-D2/D2-E1/G1 | A1/J1-J1'/A1'-E2/G2-A2/J2-J2'/A2'-G2/E2-D1/D1 (A1G1A1'E2D1,A2D2E1A2'G2|J1J1',J2J2')
8b (chiral): A1/J1-J1/A1-G1/E1-A2'/J2'-J2'/A2'-D2/D2-E1/G1 | A1'/J1'-J1'/A1'-E2/G2-A2/J2-J2/A2-G2/E2-D1/D1 (A1G1,A2'D2E1|J1,J2')/(A1'E2D1,A2G2|J1',J2)

Solution 9: A1/J1-J1/A1-H/H-C/K-L/B-I/F-D1/D1 | B/L-K/C-H/H-A2/J2-J2/A2-D2/D2-F/I
9a: A1/J1-J1/A1-H/H'-C/K-L/B-I/F-D1/D1 | B/L-K/C-H'/H-A2/J2-J2/A2-D2/D2-F/I (A1HA2D2FD1,BI,CH'|J1,KL,J2)
9b: A1/J1-J1/A1-H/H-C/K-L/B-I/F-D1/D1 | B/L-K/C-H'/H'-A2/J2-J2/A2-D2/D2-F/I (A1HCH'A2D2FD1,BI|J1,KL,J2)

Solution 10: A1/J1-J1/A1-H/H-C/K-L/B-I/F-F/I | B/L-K/C-H/H-A2/J2-J2/A2-I/F-F/I
10a: A1/J1-J1/A1-H/H'-C/K-L/B-I'/F'-F/I | B/L-K/C-H'/H-A2/J2-J2/A2-I/F-F'/I' (A1HA2I,BI',CH',FF'|J1,KL,J2)
10b: A1/J1-J1/A1-H/H'-C/K-L/B-I'/F'-F'/I' | B/L-K/C-H'/H-A2/J2-J2/A2-I/F-F/I (A1HA2IBI',CH',F,F'|J1,KL,J2)
10c: A1/J1-J1/A1-H/H-C/K-L/B-I'/F'-F/I | B/L-K/C-H'/H'-A2/J2-J2/A2-I/F-F'/I' (A1HCH'A2I,BI',FF'|J1,KL,J2)
10d: A1/J1-J1/A1-H/H-C/K-L/B-I'/F'-F'/I' | B/L-K/C-H'/H'-A2/J2-J2/A2-I/F-F/I (A1HCH'A2IBI',F,F'|J1,KL,J2)

Solution 11: A1/J1-J1/A1-H/H-C/K-L/B-D2/D2-D1/D1 | B/L-K/C-H/H-A2/J2-J2/A2-D2/D2-D1/D1
11a: A1/J1-J1/A1-H/H'-C/K-L/B-D2'/D2'-D1'/D1' | B/L-K/C-H'/H-A2/J2-J2/A2-D2/D2-D1/D1 (A1HA2D2D1BD2'D1',CH'|J1,KL,J2)
11b: A1/J1-J1/A1-H/H'-C/K-L/B-D2'/D2-D1/D1' | B/L-K/C-H'/H-A2/J2-J2/A2-D2/D2'-D1'/D1 (A1HA2D2D1BD2'D1',CH'|J1,KL,J2)
11c: A1/J1-J1/A1-H/H-C/K-L/B-D2'/D2'-D1'/D1' | B/L-K/C-H'/H'-A2/J2-J2/A2-D2/D2-D1/D1 (A1HCH'A2D2D1BD2'D1'|J1,KL,J2)
11d: A1/J1-J1/A1-H/H-C/K-L/B-D2'/D2-D1/D1' | B/L-K/C-H'/H'-A2/J2-J2/A2-D2/D2'-D1'/D1 (A1HCH'A2D2D1BD2'D1'|J1,KL,J2)

Solution 12: A1/J1-J1/A1-H/H-C/K-L/B-D2/D2-F/I | B/L-K/C-H/H-A2/J2-J2/A2-I/F-D1/D1
12a: A1/J1-J1/A1-H/H'-C/K-L/B-D2/D2-F/I | B/L-K/C-H'/H-A2/J2-J2/A2-I/F-D1/D1 (A1HA2I,BD2FD1,CH'|J1,KL,J2)
12b: A1/J1-J1/A1-H/H-C/K-L/B-D2/D2-F/I | B/L-K/C-H'/H'-A2/J2-J2/A2-I/F-D1/D1 (A1HCH'A2I,BD2FD1|J1,KL,J2)

Solution 13: A1/J1-J1/A1-H/H-A2/J2-J2/A2-I/F-D1/D1 | A1/J1-J1/A1-H/H-A2/J2-J2/A2-D2/D2-F/I
13a: A1'/J1'-J1/A1-H/H-A2/J2-J2'/A2'-I/F-D1/D1 | A1/J1-J1'/A1'-H'/H'-A2'/J2'-J2/A2-D2/D2-F/I (A1HA2D2FD1A1'H'A2'I|J1J1',J2J2')
13b: A1'/J1'-J1/A1-H/H'-A2'/J2'-J2/A2-I/F-D1/D1 | A1/J1-J1'/A1'-H'/H-A2/J2-J2'/A2'-D2/D2-F/I (A1HA2I,A1'H'A2'D2FD1|J1J1',J2J2')
13c: A1/J1-J1/A1-H/H-A2/J2-J2/A2-I/F-D1/D1 | A1'/J1'-J1'/A1'-H'/H'-A2'/J2'-J2'/A2'-D2/D2-F/I (A1HA2IA1'H'A2'D2FD1|J1,J1',J2,J2')
13d: A1/J1-J1/A1-H/H'-A2'/J2'-J2'/A2'-I/F-D1/D1 | A1'/J1'-J1'/A1'-H'/H-A2/J2-J2/A2-D2/D2-F/I (A1HA2D2FD1,A1'H'A2'I|J1,J1',J2,J2')

Solution 14: A1/J1-J1/A1-H/H-A2/J2-J2/A2-I/F-F/I (A1HA2I,F|J1,J2)

Solution 15: A1/J1-J1/A1-H/H-A2/J2-J2/A2-D2/D2-D1/D1 (A1HA2D2D1|J1,J2)

Solution 16: A1/J1-J1/A1-E2/G2-C/K-L/B-I/F-E1/G1 | B/L-K/C-G1/E1-A2/J2-J2/A2-G2/E2-F/I (A1E2FE1A2G2CG1,BI|J1,KL,J2)

Solution 17: A1/J1-J1/A1-E2/G2-C/K-L/B-G2/E2-D1/D1 | B/L-K/C-G1/E1-A2/J2-J2/A2-D2/D2-E1/G1 (A1E2D1,BG2CG1,A2D2E1|J1,KL,J2)

Solution 18: A1/J1-J1/A1-E2/G2-C/K-L/B-G2/E2-F/I | B/L-K/C-G1/E1-A2/J2-J2/A2-I/F-E1/G1 (A1E2FE1A2I,BG2CG1|J1,KL,K2)

Solution 19: A1/J1-J1/A1-E2/G2-C/K-L/B-D2/D2-E1/G1 | B/L-K/C-G1/E1-A2/J2-J2/A2-G2/E2-D1/D1 (A1E2D1BD2E1A2G2CG1|J1,KL,J2)

Solution 20: A1/J1-K/C-G1/E1-A2/J2-L/B-I/F-E1/G1 | B/L-J1/A1-E2/G2-C/K-J2/A2-G2/E2-F/I (A1E2FE1A2G2CG1,BI|J1KJ2L)

Solution 21: A1/J1-K/C-G1/E1-A2/J2-L/B-G2/E2-D1/D1 | B/L-J1/A1-E2/G2-C/K-J2/A2-D2/D2-E1/G1 (A1E2D1,BG2CG1,A2D2E1|J1KJ2L)

Solution 22: A1/J1-K/C-G1/E1-A2/J2-L/B-G2/E2-F/I | B/L-J1/A1-E2/G2-C/K-J2/A2-I/F-E1/G1 (A1E2FE1A2I,BG2CG1|J1KJ2L)

Solution 23: A1/J1-K/C-G1/E1-A2/J2-L/B-D2/D2-E1/G1 | B/L-J1/A1-E2/G2-C/K-J2/A2-G2/E2-D1/D1 (A1E2D1BD2E1A2G2CG1|J1KJ2L)

Solution 24: A1/J1-K/C-H/H-A2/J2-L/B-I/F-D1/D1 | B/L-J1/A1-H/H-C/K-J2/A2-D2/D2-F/I
24a: A1/J1-K/C-H'/H-A2/J2-L/B-I/F-D1/D1 | B/L-J1/A1-H/H'-C/K-J2/A2-D2/D2-F/I (A1HA2D2FD1,BI,CH'|J1KJ2L)
24b: A1/J1-K/C-H'/H'-A2/J2-L/B-I/F-D1/D1 | B/L-J1/A1-H/H-C/K-J2/A2-D2/D2-F/I (A1HCH'A2D2FD1,BI|J1KJ2L)

Solution 25: A1/J1-K/C-H/H-A2/J2-L/B-I/F-F/I | B/L-J1/A1-H/H-C/K-J2/A2-I/F-F/I
25a: A1/J1-K/C-H'/H-A2/J2-L/B-I'/F'-F/I | B/L-J1/A1-H/H'-C/K-J2/A2-I/F-F'/I' (A1HA2I,BI',CH',FF'|J1KJ2L)
25a: A1/J1-K/C-H'/H-A2/J2-L/B-I'/F'-F'/I' | B/L-J1/A1-H/H'-C/K-J2/A2-I/F-F/I (A1HA2IBI',CH',F,F'|J1KJ2L)
25a: A1/J1-K/C-H'/H'-A2/J2-L/B-I'/F'-F/I | B/L-J1/A1-H/H-C/K-J2/A2-I/F-F'/I' (A1HCH'A2I,BI',FF'|J1KJ2L)
25a: A1/J1-K/C-H'/H'-A2/J2-L/B-I'/F'-F'/I' | B/L-J1/A1-H/H-C/K-J2/A2-I/F-F/I (A1HCH'A2IBI',F,F'|J1KJ2L)

Solution 26: A1/J1-K/C-H/H-A2/J2-L/B-D2/D2-D1/D1 | B/L-J1/A1-H/H-C/K-J2/A2-D2/D2-D1/D1
26a: A1/J1-K/C-H'/H-A2/J2-L/B-D2'/D2'-D1'/D1' | B/L-J1/A1-H/H'-C/K-J2/A2-D2/D2-D1/D1 (A1HA2D2D1BD2'D1',CH'|J1KJ2L)
26b: A1/J1-K/C-H'/H-A2/J2-L/B-D2'/D2-D1/D1' | B/L-J1/A1-H/H'-C/K-J2/A2-D2/D2'-D1'/D1 (A1HA2D2D1BD2'D1',CH'|J1KJ2L)
26c: A1/J1-K/C-H'/H'-A2/J2-L/B-D2'/D2'-D1'/D1' | B/L-J1/A1-H/H-C/K-J2/A2-D2/D2-D1/D1 (A1HCH'A2D2D1BD2'D1'|J1KJ2L)
26d: A1/J1-K/C-H'/H'-A2/J2-L/B-D2'/D2-D1/D1' | B/L-J1/A1-H/H-C/K-J2/A2-D2/D2'-D1'/D1 (A1HCH'A2D2D1BD2'D1'|J1KJ2L)

Solution 27: A1/J1-K/C-H/H-A2/J2-L/B-D2/D2-F/I | B/L-J1/A1-H/H-C/K-J2/A2-I/F-D1/D1
27a: A1/J1-K/C-H'/H-A2/J2-L/B-D2/D2-F/I | B/L-J1/A1-H/H'-C/K-J2/A2-I/F-D1/D1 (A1HA2I,BD2FD1,CH'|J1KJ2L)
27b: A1/J1-K/C-H'/H'-A2/J2-L/B-D2/D2-F/I | B/L-J1/A1-H/H-C/K-J2/A2-I/F-D1/D1 (A1HCH'A2I,BD2FD1|J1KJ2L)

Solution 28: A1/J1-K/C-E2/G2-A2/J2-L/B-I/F-E1/G1 | B/L-J1/A1-G1/E1-C/K-J2/A2-G2/E2-F/I (A1G1,BI,CE2FE1,A2G2|J1KJ2L)

Solution 29: A1/J1-K/C-E2/G2-A2/J2-L/B-G2/E2-D1/D1 | B/L-J1/A1-G1/E1-C/K-J2/A2-D2/D2-E1/G1 (A1G1BG2A2D2E1CE2D1|J1KJ2L)

Solution 20: A1/J1-K/C-E2/G2-A2/J2-L/B-G2/E2-F/I | B/L-J1/A1-G1/E1-C/K-J2/A2-I/F-E1/G1 (A1G1BG2A2I,CE2FE1|J1KJ2L)

Solution 31: A1/J1-K/C-E2/G2-A2/J2-L/B-D2/D2-E1/G1 | B/L-J1/A1-G1/E1-C/K-J2/A2-G2/E2-D1/D1 (A1G1,BD2E1CE2D1,A2G2|J1KJ2L)

Solution 32: B/L-K/C-G1/E1-C/K-L/B-I/F-E1/G1 | B/L-K/C-E2/G2-C/K-L/B-G2/E2-F/I
32a: B'/L'-K/C-G1/E1-C'/K'-L/B-I/F-E1/G1 | B/L-K'/C'-E2/G2-C/K-L'/B'-G2/E2-F/I (BI,B'G2CG1,C'E2FE1|KL',K'L)
32b: B'/L'-K'/C'-G1/E1-C'/K'-L/B-I/F-E1/G1 | B/L-K/C-E2/G2-C/K-L'/B'-G2/E2-F/I (BI,B'G2CE2FE1C'G1|KL'K'L)
32c: B/L-K/C-G1/E1-C'/K'-L/B-I/F-E1/G1 | B'/L'-K'/C'-E2/G2-C/K-L'/B'-G2/E2-F/I (BIB'G2CG1,C'E2FE1|KL'K'L)
32d: B/L-K'/C'-G1/E1-C'/K'-L/B-I/F-E1/G1 | B'/L'-K/C-E2/G2-C/K-L'/B'-G2/E2-F/I (BIB'G2CE2FE1C'G1|KL',K'L)

Solution 33: B/L-K/C-G1/E1-C/K-L/B-G2/E2-D1/D1 | B/L-K/C-E2/G2-C/K-L/B-D2/D2-E1/G1
33a: B'/L'-K/C-G1/E1-C'/K'-L/B-G2/E2-D1/D1 | B/L-K'/C'-E2/G2-C/K-L'/B'-D2/D2-E1/G1 (BG2CG1,B'D2E1C'E2D1|KL',K'L)
33b: B'/L'-K'/C'-G1/E1-C'/K'-L/B-G2/E2-D1/D1 | B/L-K/C-E2/G2-C/K-L'/B'-D2/D2-E1/G1 (BG2CE2D1B'D2E1C'G1|KL'K'L)
33c: B/L-K/C-G1/E1-C'/K'-L/B-G2/E2-D1/D1 | B'/L'-K'/C'-E2/G2-C/K-L'/B'-D2/D2-E1/G1 (BG2CG1B'D2E1C'E2D1|KL'K'L)
33d: B/L-K'/C'-G1/E1-C'/K'-L/B-G2/E2-D1/D1 | B'/L'-K/C-E2/G2-C/K-L'/B'-D2/D2-E1/G1 (BG2CE2D1,B'D2E1C'G1|KL',K'L)

Solution 34: B/L-K/C-G1/E1-C/K-L/B-G2/E2-F/I | B/L-K/C-E2/G2-C/K-L/B-I/F-E1/G1
34a: B/L-K/C-G1/E1-C'/K'-L'/B'-G2/E2-F/I | B'/L'-K'/C'-E2/G2-C/K-L/B-I/F-E1/G1 (BI,B'G2CG1,C'E2FE1|KL,K'L')
34b: B/L-K'/C'-G1/E1-C'/K'-L'/B'-G2/E2-F/I | B'/L'-K/C-E2/G2-C/K-L/B-I/F-E1/G1 (BI,B'G2CE2FE1C'G1|KLK'L')
34c: B'/L'-K/C-G1/E1-C'/K'-L'/B'-G2/E2-F/I | B/L-K'/C'-E2/G2-C/K-L/B-I/F-E1/G1 (BIB'G2CG1,C'E2FE1|KLK'L')
34d: B'/L'-K'/C'-G1/E1-C'/K'-L'/B'-G2/E2-F/I | B/L-K/C-E2/G2-C/K-L/B-I/F-E1/G1 (BIB'G2CE2FE1C'G1|KL,K'L')

Solution 35: B/L-K/C-G1/E1-C/K-L/B-D2/D2-E1/G1 | B/L-K/C-E2/G2-C/K-L/B-G2/E2-D1/D1
35a: B/L-K/C-G1/E1-C'/K'-L'/B'-D2/D2-E1/G1 | B'/L'-K'/C'-E2/G2-C/K-L/B-G2/E2-D1/D1 (BG2CG1,B'D2E1C'E2D1|KL,K'L')
35b: B/L-K'/C'-G1/E1-C'/K'-L'/B'-D2/D2-E1/G1 | B'/L'-K/C-E2/G2-C/K-L/B-G2/E2-D1/D1 (BG2CE2D1B'D2E1C'G1|KLK'L')
35c: B'/L'-K/C-G1/E1-C'/K'-L'/B'-D2/D2-E1/G1 | B/L-K'/C'-E2/G2-C/K-L/B-G2/E2-D1/D1 (BG2CG1B'D2E1C'E2D1|KLK'L')
35d: B'/L'-K'/C'-G1/E1-C'/K'-L'/B'-D2/D2-E1/G1 | B/L-K/C-E2/G2-C/K-L/B-G2/E2-D1/D1 (BG2CE2D1,B'D2E1C'G1|KL,K'L')

Solution 36: B/L-K/C-H/H-C/K-L/B-I/F-D1/D1 | B/L-K/C-H/H-C/K-L/B-D2/D2-F/I
36a: B'/L'-K/C-H/H'-C'/K'-L/B-I/F-D1/D1 | B/L-K'/C'-H'/H-C/K-L'/B'-D2/D2-F/I (BI,B'D2FD1,CH,C'H'|KL',K'L)
36b: B'/L'-K/C-H/H-C'/K'-L/B-I/F-D1/D1 | B/L-K'/C'-H'/H'-C/K-L'/B'-D2/D2-F/I (BI,B'D2FD1,CHC'H'|KL',K'L)
36c: B'/L'-K/C-H/H-C/K-L/B-I/F-D1/D1 | B/L-K'/C'-H'/H'-C'/K'-L'/B'-D2/D2-F/I (BI,B'D2FD1,CH,C'H'|KLK'L')
36d: B'/L'-K/C-H/H'-C/K-L/B-I/F-D1/D1 | B/L-K'/C'-H'/H-C'/K'-L'/B'-D2/D2-F/I (BI,B'D2FD1,CHC'H'|KLK'L')
36e: B/L-K/C-H/H-C/K-L/B-I/F-D1/D1 | B'/L'-K'/C'-H'/H'-C'/K'-L'/B'-D2/D2-F/I (BIB'D2FD1,CH,C'H'|KL,K'L')
36f: B/L-K/C-H/H'-C/K-L/B-I/F-D1/D1 | B'/L'-K'/C'-H'/H-C'/K'-L'/B'-D2/D2-F/I (BIB'D2FD1,CHC'H'|KL,K'L')
36g: B/L-K/C-H/H'-C'/K'-L/B-I/F-D1/D1 | B'/L'-K'/C'-H'/H-C/K-L'/B'-D2/D2-F/I (BIB'D2FD1,CH,C'H'|KL'K'L)
36h: B/L-K/C-H/H-C'/K'-L/B-I/F-D1/D1 | B'/L'-K'/C'-H'/H'-C/K-L'/B'-D2/D2-F/I (BIB'D2FD1,CHC'H'|KL'K'L)

Solution 37: B/L-K/C-H/H-C/K-L/B-I/F-F/I (BI,CH,F|KL)

Solution 38: B/L-K/C-H/H-C/K-L/B-D2/D2-D1/D1 (BD2D1,CH|KL)

2|a, 2|b: 37

4|a: 14
4|a, 2|b: 1, 10a, 12a, 32a, 34a, 36a, 36b
4|a, 4|b: 25a, 27a, 28, 36c, 36d

5|a: 6b, 15
5|a, 2|b: 8a, 33d, 35d

6|a: 5b, 8b
6|a, 2|b: 4, 6a, 7a, 9a, 10b, 10c, 35a, 36e, 38
6|a, 4|b: 24a, 25b, 25c, 31, 36g

8|a, 2|b: 9b, 10d, 11a, 11b, 16
8|a, 4|b: 20, 24b, 25d, 26a, 26b, 32b, 34b

10|a: 7b
10|a, 2|b: 2, 5a, 11c, 11d, 13a, 13c, 19, 32d, 33b, 34d
10|a, 4|b: 23, 26c, 26d, 29, 33c, 35b, 35c

12|a, 2|b: 3, 12b, 13b, 13d, 17, 18, 36f
12|a, 4|b: 21, 22, 27b, 30, 32c, 33a, 34c, 36h
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Fri Apr 10, 2015 5:21 am

Type AAAABBB:

Edge data:
Code: Select all
b b b b b
a       a
a a A a a : A xK -G,E2,B2

b b a a a
b       b
a a A b b : B1 xB1 -A

b b a a b
b       b
a a A a b : C1 xE1 -B1,C1,D

b b a b b
b       b
a a A a a : D xG -E1,F,C2

b a a a a
b       b
b a A b b : E1 xC1 -A

b a a a b
b       b
b a A a b : F xF -B1,C1,D

b a a b b
b       b
b a A a a : C2 xE2 -E1,F,C2

a a a a a
b       b
b b A b b : G xD -A

a a a a b
b       b
b b A a b : E2 xC2 -B1,C1,D

a a a b b
b       b
b b A a a : B2 xB2 -E1,F,C2

a b b a a
a       a
a a B b a : H1 xH1 -J,H2

a b b b a
a       a
a a B a a : I xJ -K

a a b a a
a       a
a b B b a : J xI -J,H2

a a b b a
a       a
a b B a a : H2 xH2 -K

a a a a a
a       a
b b B b b : K xA -H1,I


Vertex sequence:
A/K
H1/H1 I/J
J/I H2/H2
K/A
G/D E2/C2 B2/B2
E1/C1 F/F C2/E2
B1/B1 C1/E1 D/G

108 possible sequences, leading to 26 basic solutions:

Solution 1: A/K-H1/H1-J/I-K/A-G/D-E1/C1-C1/E1 | A/K-I/J-H2/H2-K/A-E2/C2-C2/E2-D/G
1a: A'/K'-H1/H1-J/I-K/A-G/D-E1/C1-C1/E1 | A/K-I/J-H2/H2-K'/A'-E2/C2-C2/E2-D/G (AG,A'E2DE1,C1,C2|H1JH2K',IK)
1b: A/K-H1/H1-J/I-K/A-G/D-E1/C1-C1/E1 | A'/K'-I/J-H2/H2-K'/A'-E2/C2-C2/E2-D/G (AGA'E2DE1,C1,C2|H1JH2K'IK)

Solution 2: A/K-H1/H1-J/I-K/A-G/D-F/F-B1/B1 | A/K-I/J-H2/H2-K/A-B2/B2-F/F-D/G
2a: A'/K'-H1/H1-J/I-K/A-G/D-F'/F-B1/B1 | A/K-I/J-H2/H2-K'/A'-B2/B2-F/F'-D/G (AG,A'B2FB1,DF'|H1JH2K',IK)
2b: A'/K'-H1/H1-J/I-K/A-G/D-F'/F'-B1/B1 | A/K-I/J-H2/H2-K'/A'-B2/B2-F/F-D/G (AG,A'B2FDF'B1|H1JH2K',IK)
2c: A/K-H1/H1-J/I-K/A-G/D-F'/F-B1/B1 | A'/K'-I/J-H2/H2-K'/A'-B2/B2-F/F'-D/G (AGA'B2FB1,DF'|H1JH2K'IK)
2d: A/K-H1/H1-J/I-K/A-G/D-F'/F'-B1/B1 | A'/K'-I/J-H2/H2-K'/A'-B2/B2-F/F-D/G (AGA'B2FDF'B1|H1JH2K'IK)

Solution 3: A/K-H1/H1-J/I-K/A-G/D-F/F-D/G | A/K-I/J-H2/H2-K/A-G/D-F/F-D/G
3a: A'/K'-H1/H1-J/I-K/A-G/D-F/F'-D'/G' | A/K-I/J-H2/H2-K'/A'-G'/D'-F'/F-D/G (AG,A'G',DF,D'F'|H1JH2K',KI)
3b: A'/K'-H1/H1-J/I-K/A-G/D-F/F-D'/G' | A/K-I/J-H2/H2-K'/A'-G'/D'-F'/F'-D/G (AG,A'G',DFD'F'|H1JH2K',KI)
3c: A'/K'-H1/H1-J/I-K/A-G/D-F/F-D/G | A/K-I/J-H2/H2-K'/A'-G'/D'-F'/F'-D'/G' (AGA'G',DF,D'F'|H1JH2K',KI)
3d: A'/K'-H1/H1-J/I-K/A-G/D-F/F'-D/G | A/K-I/J-H2/H2-K'/A'-G'/D'-F'/F-D'/G' (AGA'G',DFD'F'|H1JH2K',KI)
3e: A/K-H1/H1-J/I-K/A-G/D-F/F-D/G | A'/K'-I/J-H2/H2-K'/A'-G'/D'-F'/F'-D'/G' (AG,A'G',DF,D'F'|H1JH2K'IK)
3f: A/K-H1/H1-J/I-K/A-G/D-F/F'-D/G | A'/K'-I/J-H2/H2-K'/A'-G'/D'-F'/F-D'/G' (AG,A'G',DFD'F'|H1JH2K'IK)
3g: A/K-H1/H1-J/I-K/A-G/D-F/F'-D'/G' | A'/K'-I/J-H2/H2-K'/A'-G'/D'-F'/F-D/G (AGA'G',DF,D'F'|H1JH2K'IK)
3h: A/K-H1/H1-J/I-K/A-G/D-F/F-D'/G' | A'/K'-I/J-H2/H2-K'/A'-G'/D'-F'/F'-D/G (AGA'G',DFD'F'|H1JH2K'IK)

Solution 4: A/K-H1/H1-J/I-K/A-G/D-C2/E2-C1/E1 | A/K-I/J-H2/H2-K/A-E2/C2-E1/C1-D/G
4a: A'/K'-H1/H1-J/I-K/A-G/D-C2/E2-C1/E1 | A/K-I/J-H2/H2-K'/A'-E2/C2-E1/C1-D/G (AG,A'E2C1DC2E1|H1JH2K',IK)
4b: A/K-H1/H1-J/I-K/A-G/D-C2/E2-C1/E1 | A'/K'-I/J-H2/H2-K'/A'-E2/C2-E1/C1-D/G (AGA'E2C1DC2E1|H1JH2K'IK)

Solution 5:A/K-H1/H1-J/I-K/A-E2/C2-E1/C1-B1/B1 | A/K-I/J-H2/H2-K/A-B2/B2-C2/E2-C1/E1
5a: A'/K'-H1/H1-J/I-K/A-E2/C2-E1/C1-B1/B1 | A/K-I/J-H2/H2-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1A'B2C2E1|H1JH2K',IK)
5b: A/K-H1/H1-J/I-K/A-E2/C2-E1/C1-B1/B1 | A'/K'-I/J-H2/H2-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1,A'B2C2E1|H1JH2K'IK)

Solution 6: A/K-H1/H1-J/I-K/A-E2/C2-E1/C1-D/G | A/K-I/J-H2/H2-K/A-G/D-C2/E2-C1/E1
6a: A/K-H1/H1-J/I-K'/A'-E2/C2-E1/C1-D/G | A'/K'-I/J-H2/H2-K/A-G/D-C2/E2-C1/E1 (AG,A'E2C1DC2E1|H1JH2K,IK')
6b: A'/K'-H1/H1-J/I-K'/A'-E2/C2-E1/C1-D/G | A/K-I/J-H2/H2-K/A-G/D-C2/E2-C1/E1 (AGA'E2C1DC2E1|H1JH2KIK')

Solution 7: A/K-H1/H1-J/I-K/A-E2/C2-C2/E2-B1/B1 | A/K-I/J-H2/H2-K/A-B2/B2-E1/C1-C1/E1
7a: A'/K'-H1/H1-J/I-K/A-E2/C2-C2/E2-B1/B1 | A/K-I/J-H2/H2-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1A'B2E1,C1,C2|H1JH2K',IK)
7b: A/K-H1/H1-J/I-K/A-E2/C2-C2/E2-B1/B1 | A'/K'-I/J-H2/H2-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1,A'B2E1,C1,C2|H1JH2K'IK)

Solution 8: A/K-H1/H1-J/I-K/A-E2/C2-C2/E2-D/G | A/K-I/J-H2/H2-K/A-G/D-E1/C1-C1/E1
8a: A/K-H1/H1-J/I-K'/A'-E2/C2-C2/E2-D/G | A'/K'-I/J-H2/H2-K/A-G/D-E1/C1-C1/E1 (AG,A'E2DE1,C1,C2|H1JH2K,IK')
8b: A'/K'-H1/H1-J/I-K'/A'-E2/C2-C2/E2-D/G | A/K-I/J-H2/H2-K/A-G/D-E1/C1-C1/E1 (AGA'E2DE1,C1,C2|H1JH2KIK')

Solution 9: A/K-H1/H1-J/I-K/A-B2/B2-E1/C1-C1/E1 | A/K-I/J-H2/H2-K/A-E2/C2-C2/E2-B1/B1
9a: A/K-H1/H1-J/I-K'/A'-B2/B2-E1/C1-C1/E1 | A'/K'-I/J-H2/H2-K/A-E2/C2-C2/E2-B1/B1 (AE2B1A'B2E1,C1,C2|H1JH2K,IK')
9b: A'/K'-H1/H1-J/I-K'/A'-B2/B2-E1/C1-C1/E1 | A/K-I/J-H2/H2-K/A-E2/C2-C2/E2-B1/B1 (AE2B1,A'B2E1,C1,C2|H1JH2KIK')

Solution 10: A/K-H1/H1-J/I-K/A-B2/B2-F/F-B1/B1 | A/K-I/J-H2/H2-K/A-B2/B2-F/F-B1/B1
10a: A'/K'-H1/H1-J/I-K/A-B2/B2-F/F-B1/B1 | A/K-I/J-H2/H2-K'/A'-B2'/B2'-F'/F'-B1'/B1' (AB2FB1A'B2'F'B1'|H1JK2K',IK)
10b: A'/K'-H1/H1-J/I-K/A-B2/B2-F/F'-B1'/B1' | A/K-I/J-H2/H2-K'/A'-B2'/B2'-F'/F-B1/B1 (AB2FB1,A'B2'F'B1'|H1JK2K',IK)
10c: A'/K'-H1/H1-J/I-K/A-B2/B2'-F'/F'-B1'/B1 | A/K-I/J-H2/H2-K'/A'-B2'/B2-F/F-B1/B1' (AB2FB1A'B2'F'B1'|H1JK2K',IK)
10d: A'/K'-H1/H1-J/I-K/A-B2/B2'-F'/F-B1/B1' | A/K-I/J-H2/H2-K'/A'-B2'/B2-F/F'-B1'/B1 (AB2FB1,A'B2'F'B1'|H1JK2K',IK)
10e: A/K-H1/H1-J/I-K/A-B2/B2-F/F-B1/B1 | A'/K'-I/J-H2/H2-K'/A'-B2'/B2'-F'/F'-B1'/B1' (AB2FB1,A'B2'F'B1'|H1JK2K'IK)
10f: A/K-H1/H1-J/I-K/A-B2/B2-F/F'-B1'/B1' | A'/K'-I/J-H2/H2-K'/A'-B2'/B2'-F'/F-B1/B1 (AB2FB1A'B2'F'B1'|H1JK2K'IK)
10g: A/K-H1/H1-J/I-K/A-B2/B2'-F'/F'-B1'/B1 | A'/K'-I/J-H2/H2-K'/A'-B2'/B2-F/F-B1/B1' (AB2FB1,A'B2'F'B1'|H1JK2K'IK)
10h: A/K-H1/H1-J/I-K/A-B2/B2'-F'/F-B1/B1' | A'/K'-I/J-H2/H2-K'/A'-B2'/B2-F/F'-B1'/B1 (AB2FB1A'B2'F'B1'|H1JK2K'IK)

Solution 11: A/K-H1/H1-J/I-K/A-B2/B2-F/F-D/G | A/K-I/J-H2/H2-K/A-G/D-F/F-B1/B1
11a: A/K-H1/H1-J/I-K'/A'-B2/B2-F/F'-D/G | A'/K'-I/J-H2/H2-K/A-G/D-F'/F-B1/B1 (AG,A'B2FB1,DF'|H1JH2K,IK')
11b: A/K-H1/H1-J/I-K'/A'-B2/B2-F/F-D/G | A'/K'-I/J-H2/H2-K/A-G/D-F'/F'-B1/B1 (AG,A'B2FDF'B1|H1JH2K,IK')
11c: A'/K'-H1/H1-J/I-K'/A'-B2/B2-F/F'-D/G | A/K-I/J-H2/H2-K/A-G/D-F'/F-B1/B1 (AGA'B2FB1,DF'|H1JH2KIK')
11d: A'/K'-H1/H1-J/I-K'/A'-B2/B2-F/F-D/G | A/K-I/J-H2/H2-K/A-G/D-F'/F'-B1/B1 (AGA'B2FDF'B1|H1JH2KIK')

Solution 12: A/K-H1/H1-J/I-K/A-B2/B2-C2/E2-C1/E1 | A/K-I/J-H2/H2-K/A-E2/C2-E1/C1-B1/B1
12a: A/K-H1/H1-J/I-K'/A'-B2/B2-C2/E2-C1/E1 | A'/K'-I/J-H2/H2-K/A-E2/C2-E1/C1-B1/B1 (AE2C1B1A'B2C2E1|H1JH2K,IK')
12b: A'/K'-H1/H1-J/I-K'/A'-B2/B2-C2/E2-C1/E1 | A/K-I/J-H2/H2-K/A-E2/C2-E1/C1-B1/B1 (AE2C1B1,A'B2C2E1|H1JH2KIK')

Solution 13: A/K-H1/H1-H2/H2-K/A-G/D-E1/C1-C1/E1 | A/K-H1/H1-H2/H2-K/A-E2/C2-C2/E2-D/G
13a: A'/K'-H1/H1-H2/H2-K/A-G/D-E1/C1-C1/E1 | A/K-H1'/H1'-H2'/H2'-K'/A'-E2/C2-C2/E2-D/G (AG,A'E2DE1,C1,C2|H1H2KH1'H2'K')
13b: A'/K'-H1'/H1-H2/H2'-K/A-G/D-E1/C1-C1/E1 | A/K-H1/H1'-H2'/H2-K'/A'-E2/C2-C2/E2-D/G (AG,A'E2DE1,C1,C2|H1H2K'H1'H2'K)
13c: A/K-H1/H1-H2/H2-K/A-G/D-E1/C1-C1/E1 | A'/K'-H1'/H1'-H2'/H2'-K'/A'-E2/C2-C2/E2-D/G (AGA'E2DE1,C1,C2|H1H2K,H1'H2'K')
13d: A/K-H1'/H1-H2/H2'-K/A-G/D-E1/C1-C1/E1 | A'/K'-H1/H1'-H2'/H2-K'/A'-E2/C2-C2/E2-D/G (AGA'E2DE1,C1,C2|H1H2K',H1'H2'K)

Solution 14: A/K-H1/H1-H2/H2-K/A-G/D-F/F-B1/B1 | A/K-H1/H1-H2/H2-K/A-B2/B2-F/F-D/G
14a: A'/K'-H1/H1-H2/H2-K/A-G/D-F'/F-B1/B1 | A/K-H1'/H1'-H2'/H2'-K'/A'-B2/B2-F/F'-D/G (AG,A'B2FB1,DF'|H1H2KH1'H2'K')
14b: A'/K'-H1'/H1-H2/H2'-K/A-G/D-F'/F-B1/B1 | A/K-H1/H1'-H2'/H2-K'/A'-B2/B2-F/F'-D/G (AG,A'B2FB1,DF'|H1H2K'H1'H2'K)
14c: A'/K'-H1/H1-H2/H2-K/A-G/D-F'/F'-B1/B1 | A/K-H1'/H1'-H2'/H2'-K'/A'-B2/B2-F/F-D/G (AG,A'B2FDF'B1|H1H2KH1'H2'K')
14d: A'/K'-H1'/H1-H2/H2'-K/A-G/D-F'/F'-B1/B1 | A/K-H1/H1'-H2'/H2-K'/A'-B2/B2-F/F-D/G (AG,A'B2FDF'B1|H1H2K'H1'H2'K)
14e: A/K-H1/H1-H2/H2-K/A-G/D-F'/F-B1/B1 | A'/K'-H1'/H1'-H2'/H2'-K'/A'-B2/B2-F/F'-D/G (AGA'B2FB1,DF'|H1H2K,K'H1'H2')
14f: A/K-H1'/H1-H2/H2'-K/A-G/D-F'/F-B1/B1 | A'/K'-H1/H1'-H2'/H2-K'/A'-B2/B2-F/F'-D/G (AGA'B2FB1,DF'|H1H2K',KH1'H2')
14g: A/K-H1/H1-H2/H2-K/A-G/D-F'/F'-B1/B1 | A'/K'-H1'/H1'-H2'/H2'-K'/A'-B2/B2-F/F-D/G (AGA'B2FDF'B1|H1H2K,K'H1'H2')
14h: A/K-H1'/H1-H2/H2'-K/A-G/D-F'/F'-B1/B1 | A'/K'-H1/H1'-H2'/H2-K'/A'-B2/B2-F/F-D/G (AGA'B2FDF'B1|H1H2K',K'H1'H2')

Solution 15: A/K-H1/H1-H2/H2-K/A-G/D-F/F-D/G (AG,DF|H1H2K)

Solution 16: A/K-H1/H1-H2/H2-K/A-G/D-C2/E2-C1/E1 | A/K-H1/H1-H2/H2-K/A-E2/C2-E1/C1-D/G
16a: A'/K'-H1/H1-H2/H2-K/A-G/D-C2/E2-C1/E1 | A/K-H1'/H1'-H2'/H2'-K'/A'-E2/C2-E1/C1-D/G (AG,A'E2C1DC2E1|H1H2KH1'H2'K')
16b: A'/K'-H1'/H1-H2/H2'-K/A-G/D-C2/E2-C1/E1 | A/K-H1/H1'-H2'/H2-K'/A'-E2/C2-E1/C1-D/G (AG,A'E2C1DC2E1|H1H2K'H1'H2'K)
16c: A/K-H1/H1-H2/H2-K/A-G/D-C2/E2-C1/E1 | A'/K'-H1'/H1'-H2'/H2'-K'/A'-E2/C2-E1/C1-D/G (AGA'E2C1DC2E1|H1H2K,H1'H2'K')
16d: A/K-H1'/H1-H2/H2'-K/A-G/D-C2/E2-C1/E1 | A'/K'-H1/H1'-H2'/H2-K'/A'-E2/C2-E1/C1-D/G (AGA'E2C1DC2E1|H1H2K',H1'H2'K)

Solution 17: A/K-H1/H1-H2/H2-K/A-E2/C2-E1/C1-B1/B1 | A/K-H1/H1-H2/H2-K/A-B2/B2-C2/E2-C1/E1
17a: A'/K'-H1/H1-H2/H2-K/A-E2/C2-E1/C1-B1/B1 | A/K-H1'/H1'-H2'/H2'-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1A'B2C2E1|H1H2KH1'H2'K')
17b: A'/K'-H1'/H1-H2/H2'-K/A-E2/C2-E1/C1-B1/B1 | A/K-H1/H1'-H2'/H2-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1A'B2C2E1|H1H2K'H1'H2'K)
17c: A/K-H1/H1-H2/H2-K/A-E2/C2-E1/C1-B1/B1 | A'/K'-H1'/H1'-H2'/H2'-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1,A'B2C2E1|H1H2K,H1'H2'K')
17d: A/K-H1'/H1-H2/H2'-K/A-E2/C2-E1/C1-B1/B1 | A'/K'-H1/H1'-H2'/H2-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1,A'B2C2E1|H1H2K',H1'H2'K)

Solution 18: A/K-H1/H1-H2/H2-K/A-E2/C2-C2/E2-B1/B1 | A/K-H1/H1-H2/H2-K/A-B2/B2-E1/C1-C1/E1
18a: A'/K'-H1/H1-H2/H2-K/A-E2/C2-C2/E2-B1/B1 | A/K-H1'/H1'-H2'/H2'-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1A'B2E1,C1,C2|H1H2KH1'H2'K')
18b: A'/K'-H1'/H1-H2/H2'-K/A-E2/C2-C2/E2-B1/B1 | A/K-H1/H1'-H2'/H2-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1A'B2E1,C1,C2|H1H2K'H1'H2'K)
18c (chiral): A/K-H1/H1-H2/H2-K/A-E2/C2-C2/E2-B1/B1 | A'/K'-H1'/H1'-H2'/H2'-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1,C2|H1H2K)/(A'B2E1,C1|H1'H2'K')
18d: A/K-H1'/H1-H2/H2'-K/A-E2/C2-C2/E2-B1/B1 | A'/K'-H1/H1'-H2'/H2-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1,A'B2E1,C1,C2|H1H2K',H1'H2'K)

Solution 19: A/K-H1/H1-H2/H2-K/A-B2/B2-F/F-B1/B1 (AB2FB1|H1H2K)

Solution 20: A/K-I/J-J/I-K/A-G/D-E1/C1-C1/E1 | A/K-I/J-J/I-K/A-E2/C2-C2/E2-D/G
20a: A'/K'-I'/J'-J/I-K/A-G/D-E1/C1-C1/E1 | A/K-I/J-J'/I'-K'/A'-E2/C2-C2/E2-D/G (AG,A'E2DE1,C1,C2|IK,I'K',JJ')
20b: A'/K'-I/J-J/I-K/A-G/D-E1/C1-C1/E1 | A/K-I'/J'-J'/I'-K'/A'-E2/C2-C2/E2-D/G (AG,A'E2DE1,C1,C2|IKI'K',J,J')
20c: A/K-I/J-J/I-K/A-G/D-E1/C1-C1/E1 | A'/K'-I'/J'-J'/I'-K'/A'-E2/C2-C2/E2-D/G (AGA'E2DE1,C1,C2|IK,I'K',J,J')
20d: A/K-I'/J'-J/I-K/A-G/D-E1/C1-C1/E1 | A'/K'-I/J-J'/I'-K'/A'-E2/C2-C2/E2-D/G (AGA'E2DE1,C1,C2|IKI'K',JJ')

Solution 21: A/K-I/J-J/I-K/A-G/D-F/F-B1/B1 | A/K-I/J-J/I-K/A-B2/B2-F/F-D/G
21a: A'/K'-I'/J'-J/I-K/A-G/D-F'/F-B1/B1 | A/K-I/J-J'/I'-K'/A'-B2/B2-F/F'-D/G (AG,A'B2FB1,DF'|IK,I'K',JJ')
21b: A'/K'-I/J-J/I-K/A-G/D-F'/F-B1/B1 | A/K-I'/J'-J'/I'-K'/A'-B2/B2-F/F'-D/G (AG,A'B2FB1,DF'|IKI'K',J,J')
21c: A'/K'-I'/J'-J/I-K/A-G/D-F'/F'-B1/B1 | A/K-I/J-J'/I'-K'/A'-B2/B2-F/F-D/G (AG,A'B2FDF'B1|IK,I'K',JJ')
21d: A'/K'-I/J-J/I-K/A-G/D-F'/F'-B1/B1 | A/K-I'/J'-J'/I'-K'/A'-B2/B2-F/F-D/G (AG,A'B2FDF'B1|IKI'K',J,J')
21e: A/K-I/J-J/I-K/A-G/D-F'/F-B1/B1 | A'/K'-I'/J'-J'/I'-K'/A'-B2/B2-F/F'-D/G (AGA'B2FB1,DF'|IK,I'K',J,J')
21f: A/K-I'/J'-J/I-K/A-G/D-F'/F-B1/B1 | A'/K'-I/J-J'/I'-K'/A'-B2/B2-F/F'-D/G (AGA'B2FB1,DF'|IKI'K',JJ')
21g: A/K-I/J-J/I-K/A-G/D-F'/F'-B1/B1 | A'/K'-I'/J'-J'/I'-K'/A'-B2/B2-F/F-D/G (AGA'B2FDF'B1|IK,I'K',J,J')
21h: A/K-I'/J'-J/I-K/A-G/D-F'/F'-B1/B1 | A'/K'-I/J-J'/I'-K'/A'-B2/B2-F/F-D/G (AGA'B2FDF'B1|IKI'K',JJ')

Solution 22: A/K-I/J-J/I-K/A-G/D-F/F-D/G (AG,DF|IK,J)

Solution 23: A/K-I/J-J/I-K/A-G/D-C2/E2-C1/E1 | A/K-I/J-J/I-K/A-E2/C2-E1/C1-D/G
23a: A'/K'-I'/J'-J/I-K/A-G/D-C2/E2-C1/E1 | A/K-I/J-J'/I'-K'/A'-E2/C2-E1/C1-D/G (AG,A'E2C1DC2E1|IK,I'K',JJ')
23b: A'/K'-I/J-J/I-K/A-G/D-C2/E2-C1/E1 | A/K-I'/J'-J'/I'-K'/A'-E2/C2-E1/C1-D/G (AG,A'E2C1DC2E1|IKI'K',J,J')
23c: A/K-I/J-J/I-K/A-G/D-C2/E2-C1/E1 | A'/K'-I'/J'-J'/I'-K'/A'-E2/C2-E1/C1-D/G (AGA'E2C1DC2E1|IK,I'K',J,J')
23d: A/K-I'/J'-J/I-K/A-G/D-C2/E2-C1/E1 | A'/K'-I/J-J'/I'-K'/A'-E2/C2-E1/C1-D/G (AGA'E2C1DC2E1|IKI'K',JJ')

Solution 24: A/K-I/J-J/I-K/A-E2/C2-E1/C1-B1/B1 | A/K-I/J-J/I-K/A-B2/B2-C2/E2-C1/E1
24a: A'/K'-I'/J'-J/I-K/A-E2/C2-E1/C1-B1/B1 | A/K-I/J-J'/I'-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1A'B2C2E1|IK,I'K')
24b: A'/K'-I/J-J/I-K/A-E2/C2-E1/C1-B1/B1 | A/K-I'/J'-J'/I'-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1A'B2C2E1|IKI'K')
24c: A/K-I/J-J/I-K/A-E2/C2-E1/C1-B1/B1 | A'/K'-I'/J'-J'/I'-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1,A'B2C2E1|IK,I'K')
24d: A/K-I'/J'-J/I-K/A-E2/C2-E1/C1-B1/B1 | A'/K'-I/J-J'/I'-K'/A'-B2/B2-C2/E2-C1/E1 (AE2C1B1,A'B2C2E1|IKI'K')

Solution 25: A/K-I/J-J/I-K/A-E2/C2-C2/E2-B1/B1 | A/K-I/J-J/I-K/A-B2/B2-E1/C1-C1/E1
25a: A'/K'-I'/J'-J/I-K/A-E2/C2-C2/E2-B1/B1 | A/K-I/J-J'/I'-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1A'B2E1,C1,C2|IK,I'K',JJ')
25b: A'/K'-I/J-J/I-K/A-E2/C2-C2/E2-B1/B1 | A/K-I'/J'-J'/I'-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1A'B2E1,C1,C2|IKI'K',J,J')
25c (chiral): A/K-I/J-J/I-K/A-E2/C2-C2/E2-B1/B1 | A'/K'-I'/J'-J'/I'-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1,C2|IK,J)/(A'B2E1,C1|I'K',J')
25d: A/K-I'/J'-J/I-K/A-E2/C2-C2/E2-B1/B1 | A'/K'-I/J-J'/I'-K'/A'-B2/B2-E1/C1-C1/E1 (AE2B1,A'B2E1,C1,C2|IKI'K',JJ')

Solution 26: A/K-I/J-J/I-K/A-B2/B2-F/F-B1/B1 (AB2B1,F|IK,J)

2|a, 2|b: 22
2|a, 3|b: 15
2|a, 4|b: 3a
2|a, 6|b: 3e

3|a, 2|b: 25c, 26
3|a, 3|b: 18c, 18d
3|a, 4|b: 25d
3|a, 6|b: 7b, 9b

4|a, 2|b: 20a, 21a, 24c
4|a, 3|b: 17c, 17d, 19
4|a, 4|b: 1a, 2a, 3b, 3c, 3d, 8a, 10b, 10d, 11a, 20b, 21b, 24d
4|a, 6|b: 3f, 3g, 3h, 5b, 10e, 10g, 12b, 13a, 13b, 14a, 14b

6|a, 2|b: 20c, 21c, 21e, 23a, 25a
6|a, 3|b: 13c, 13d, 14e, 14f
6|a, 4|b: 2b, 4a, 6a, 7a, 9a, 11b, 20d, 21d, 21f, 23b, 25b
6|a, 6|b: 1b, 2c, 8b, 11c, 14c, 14d, 16a, 16b, 18a, 18b

8|a, 2|b: 21g, 23c, 24a
8|a, 3|b: 14g, 14h, 16c, 16d
8|a, 4|b: 5a, 10a, 10c, 12a, 21h, 23d, 24b
8|a, 6|b: 2d, 4b, 6b, 10f, 10h, 11d, 17a, 17b
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Fri Apr 10, 2015 5:29 pm

Note: I just found Don Hatch's hyperbolic applet (http://www.plunk.org/~hatch/HyperbolicApplet/) and managed to get it to show general tilings, so just a note about the relationship between my notation and the orbifold notation it uses.

Let's try it on first two basic tilings from the recently posted AAAABBB group:

Solution 1: A/K-H1/H1-J/I-K/A-G/D-E1/C1-C1/E1 | A/K-I/J-H2/H2-K/A-E2/C2-C2/E2-D/G
1a: A'/K'-H1/H1-J/I-K/A-G/D-E1/C1-C1/E1 | A/K-I/J-H2/H2-K'/A'-E2/C2-C2/E2-D/G (AG,A'E2DE1,C1,C2|H1JH2K',IK)
1b: A/K-H1/H1-J/I-K/A-G/D-E1/C1-C1/E1 | A'/K'-I/J-H2/H2-K'/A'-E2/C2-C2/E2-D/G (AGA'E2DE1,C1,C2|H1JH2K'IK)

Solution 2: A/K-H1/H1-J/I-K/A-G/D-F/F-B1/B1 | A/K-I/J-H2/H2-K/A-B2/B2-F/F-D/G
2a: A'/K'-H1/H1-J/I-K/A-G/D-F'/F-B1/B1 | A/K-I/J-H2/H2-K'/A'-B2/B2-F/F'-D/G (AG,A'B2FB1,DF'|H1JH2K',IK)
2b: A'/K'-H1/H1-J/I-K/A-G/D-F'/F'-B1/B1 | A/K-I/J-H2/H2-K'/A'-B2/B2-F/F-D/G (AG,A'B2FDF'B1|H1JH2K',IK)
2c: A/K-H1/H1-J/I-K/A-G/D-F'/F-B1/B1 | A'/K'-I/J-H2/H2-K'/A'-B2/B2-F/F'-D/G (AGA'B2FB1,DF'|H1JH2K'IK)
2d: A/K-H1/H1-J/I-K/A-G/D-F'/F'-B1/B1 | A'/K'-I/J-H2/H2-K'/A'-B2/B2-F/F-D/G (AGA'B2FDF'B1|H1JH2K'IK)

Step 1: write the polygon sequence around the vertex:
b-b-b-a-a-a-a | b-b-b-a-a-a-a
This shows in what order you should write the polygons in the box (you can also download the applet and run it as java -jar HyperbolicApplet.jar symbol=<symbol>)

Step 2: number the edges
0-1-2-3-4-5-6 | 3-2-1-0-6-5-4
The first edge of the first vertex is 0; the second, mirror vertex is numbered in the opposite order and you need to find where to place the 0. For all solution of the same group, this position is identical.

Step 3: starting from the edge 0, you find the position of the opposite edge (with same symbols but in switched order).
So for 1a:
Position 0: A'/K'; K'/A' is on position 0 in the right vertex, so the symbol will be [0]
Position 1: H1/H1; this is self-dual, so the opposite symbol is also on position 1 in the left vertex, so the symbol will be (1)
Position 2: J/I; I/J is on 2-right - [2]
Position 3: K/A: A/K is on 3-right - [3]
Position 4: G/D: D/G is on 4-right - [4]
Position 5: E1/C1: C1/E1 is on 6-left - (5_6) (underscores are preffered to spaces because the inline call doesn't work with spaces)
Total symbol: [0](1)[2][3][4](5_6)

For 1b: (0_3)(1)[2][4](5_6)
2a: [0](1)[2][3][4][5](6)
2b: [0](1)[2][3][4](5)(6)
2c: (0_3)(1)[2][4][5](6)
2d: (0_3)(1)[2][4](5)[6]

Unfortunately, the applet doesn't do colorings, so you have to select distinct polygons for a and b to see some result. Smallest ones are:
8,8,8,4,4,4,4 for 1a and 2a
4,4,4,6,6,6,6 for 2b
12,12,12,6,6,6,6 for 1b and 2c
6,6,6,8,8,8,8 for 2d
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Thu Mar 15, 2018 4:40 pm

Working through the results, I have now verified everything, found speficic examples and corrected some mistakes. Pushing forward.

This is one of the weirder tilings I found, just with how darn asymmetrical that vertex figure is. There are 40 solutions for this particular configuration, but this is the only one where the main polygon (appearing 4 times per vertex) is allowed to be odd.
Attachments
20180315.jpg
(257.26 KiB) Not downloaded yet
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Wed Dec 05, 2018 7:50 am

OK, I have now finished the analysis for all tilings with 7 or less polygons per vertex. Raw file is attached.

I have updated and streamlined my methods throughout the years, so I will use one of the 7-valent tilings as an example here to explain what the symbols mean:

AABCBDE - type of the tiling. The hierarchy is:
1. Valency (how many polygons meet at each vertex). Here, it's 7.
2. Variety (how many different polygons exist in the tiling). Here, it's 5 (A,B,C,D,E).
3. Kind (the exact proportions of the various polygons). Here, it's AABBCDE -- A and B occur twice per vertex while C, D, and E each occurs once.
4. Type (the exact configuration) For each kind, I enumerated cyclic permutations of the symbols with the caveat that two permutations are also considered identical if you can transform one into the other by relabeling. In this particular kind, swapping A and B and/or any permutation on C, D, and E makes no difference. "Type" is the lexicographically first permutation among all possibilities.

This particular kind has 12 distinct types:

AABBCDE
AABCBDE
AABCDBE
AABCDEB
AACBBDE
AACBDBE
ABABCDE
ABACBDE
ABCABDE
ABCADBE
ABCBADE
ABCBDAE

Edge data:
Here, I enumerate possible edges of the tiling. Each edge is a combination of 2 vertex configurations. They are in code block because it's important to view them in non-proportional font. Each edge gets labeled with a capital letter (if more than 26 types exist, I start using labels Aa, Ba, Ca, etc.) Chiral edges get marked with "1" or "2" suffix (for example C1 and C2 are a chiral pair).

The string "A xQ -E,C2", for example means this:

1. The edge is labeled A.
2. The opposite edge is Q (each edge A, that belongs to an A-gon, matches up to a Q-edge on an E-gon).
3. If a polygon has edge A, the following edge must be either E or C2.

In this particular kind, the edges are:
Edges between 2 A-gons (C1/C1, D/E, C2/C2)
Edges between A-gon and B-gon (B/I)
Edges between A-gon and E-gon (A/Q)
Edges between B-gon and C-gon (F1/K1, G/M, J/L, F2/K2)
Edges between B-gon and D-gon (H/O)
Edges between D-gon and E-gon (N/P)

Code: Select all
b d e d b
c       c
b a A a b : A xQ -E,C2

b c b c b
d       d
e a A a e : B xI -C1,D

d e a b c
b       b
c b A e d : C1 xC1 -A

d e a e d
b       b
c b A b c : D xE -B

c b a b c
b       b
d e A e d : E xD -A

c b a e d
b       b
d e A b c : C2 xC2 -B

d b c b a
e       a
a a B d e : F1 xK1 -H

d b c b d
e       e
a a B a a : G xM -I

a e d e a
a       a
b c B c b : H xO -J,F2

e a a a e
d       d
b c B c b : I xB -F1,G

a b c b a
a       a
e d B d e : J xL -H

a b c b d
a       e
e d B a a : F2 xK2 -I

e d b a a
a       e
a b C b d : K1 xF1 -K1,L

e d b d e
a       a
a b C b a : L xJ -M,K2

a a b a a
e       e
d b C b d : M xG -K1,L

a a b d e
e       a
d b C b a : K2 xF2 -M,K2

a a e a a
b       b
c b D b c : N xP -O

b c b c b
a       a
a e D e a : O xH -N

c b d b c
b       b
a a E a a : P xN -Q

b a a a b
c       c
b d E d b : Q xA -P


Vertex sequence:
A/Q
P/N
O/H
J/L F2/K2
M/G K2/F2
I/B
C1/C1 D/E

Reverse vertex sequence:
B/I
F1/K1 G/M
K1/F1 L/J
H/O
N/P
Q/A
E/D C2/C2

Vertex sequences are built by starting with first possible edge (here A/Q). Then I find possible followers for Q -- the only option is P, so next row is P/N. Even if there are multiple options in one row, they must all share the same followers.
There is one important thing here: some kinds, like this one, are inherently asymmetrical -- that means I build two vertex sequences with one being mirror image of the other. That's the easier way. If the kind is formed by a symmetrical sequence, the situation is more complicated and I'll cover that in next post.

8 possible sequences, leading to 4 solutions:
Now I just enumerate the possible sequences. I want the tiling to be uniform, which means that I need to eliminate combinations that don't close properly. This particular kind is easy: I just need to make sure that the F/K edges are paired correctly -- either the sequence must contain both F2/K2 and K2/F2, or it must contain neither.

Solution 1: A/Q-P/N-O/H-J/L-M/G-I/B-C1/C1 | B/I-G/M-L/J-H/O-N/P-Q/A-C2/C2 (AC2BC1|GI,HJ|LM|NO|PQ)
Solution 2: A/Q-P/N-O/H-J/L-M/G-I/B-D/E | B/I-G/M-L/J-H/O-N/P-Q/A-E/D (AE,BD|GI,HJ|LM|NO|PQ)
Solution 3: A/Q-P/N-O/H-F2/K2-K2/F2-I/B-C1/C1 | B/I-F1/K1-K1/F1-H/O-N/P-Q/A-C2/C2 (AC2BC1|F1HF2I|K1,K2|NO|PQ)
Solution 4: A/Q-P/N-O/H-F2/K2-K2/F2-I/B-D/E | B/I-F1/K1-K1/F1-H/O-N/P-Q/A-E/D (AE,BD|F1HF2I|K1,K2|NO|PQ)

Each solution is a particular instance of vertex sequence and its corresponding reverse vertex sequence. The exact configuration for the polygons is read from this sequence.

2|a, 2|b, 2|c, 2|d, 2|e: 2
"(12,10,6,8,6,4,4)"
2|a, 4|b, 2|d, 2|e: 4
"(10,8,4,3,4,6,6) (3 4)"

4|a, 2|b, 2|c, 2|d, 2|e: 1
"(12,10,6,8,6,4,4) (6)"
4|a, 4|b, 2|d, 2|e: 3
"(10,6,8,3,8,4,4) (3 4)(6)"

This last part just shows conditions for existence of various solutions, together with an example of such solution in Conway notation that can be inputted into Hyperbolic applet (or, at this point, to HyperRogue).
Attachments
tilings.txt
(589.21 KiB) Not downloaded yet
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Re: Hyperbolic Tilings

Postby Marek14 » Wed Dec 05, 2018 8:09 am

So, let's have a look what happens if the kind is formed by a symmetrical sequence, shall we? I'll use ABABACC as an example:

ABABACC

Edge data:
Code: Select all
a c c c a
b       b
a b A b a : A xI -D,B2

c a b a b
c       a
a b A c c : B1 xE1 -A

c a b a c
c       c
a b A b a : C xG -B1,C

b a b a b
a       a
c c A c c : D xF -A

b a b a c
a       c
c c A b a : B2 xE2 -B1,C

c c a b a
a       c
b a B a c : E1 xB1 -E1,F

c c a c c
a       a
b a B a b : F xD -G,E2

a b a b a
c       c
c a B a c : G xC -E1,F

a b a c c
c       a
c a B a b : E2 xB2 -G,E2

b a c a b
a       a
b a C a b : H xH -I

a b a b a
b       b
a c C c a : I xA -H


You will notice that the edge data tend to be significantly smaller for symmetrical kinds. Without chirality, the possibilities are reduced.

Vertex sequence:
A/I
H/H
I/A
D/F B2/E2
G/C E2/B2
B1/E1 C/G
E1/B1 F/D

No reverse vertex sequence since the regular sequence is symmetrical.

16 possible sequences, leading to 4 basic solutions:

Solution 1: A/I-H/H-I/A-D/F-G/C-B1/E1-E1/B1 | A/I-H/H-I/A-B2/E2-E2/B2-C/G-F/D
And here it starts being complicated. Even though the kind is symmetrical, it doesn't mean that the particular solution will be. Often, we have to use two mirrored sequences to form a complete solution.
However, some edges (A/I, H/H, and I/A) occur once in each half. This means there is no longer a unique way to join them up. The solution I eventually came up with is to use primes (') to distinguish between them. Since there are multiple ways to introduce them, the sequence (basic solution) splits into a number of individual solutions. Here, there are four because there are two ways to pair A/I edges and two ways to pair H edges.

1a: A/I-H/H'-I'/A'-D/F-G/C-B1/E1-E1/B1 | A'/I'-H'/H-I/A-B2/E2-E2/B2-C/G-F/D (AB2CB1,A'D|E1,FG,E2|HI,H'I')
1b: A/I-H/H-I'/A'-D/F-G/C-B1/E1-E1/B1 | A'/I'-H'/H'-I/A-B2/E2-E2/B2-C/G-F/D (AB2CB1,A'D|E1,FG,E2|HI'H'I)
1c: A/I-H/H-I/A-D/F-G/C-B1/E1-E1/B1 | A'/I'-H'/H'-I'/A'-B2/E2-E2/B2-C/G-F/D (ADA'B2CB1|E1,FG,E2|HI,H'I')
1d: A/I-H/H'-I/A-D/F-G/C-B1/E1-E1/B1 | A'/I'-H'/H-I'/A'-B2/E2-E2/B2-C/G-F/D (ADA'B2CB1|E1,FG,E2|HI'H'I)

Solution 2: A/I-H/H-I/A-D/F-G/C-C/G-F/D (AD,C|FG|HI)
On the other hand, this basic solution is truly symmetrical, and so it can't be split.

Solution 3: A/I-H/H-I/A-D/F-E2/B2-C/G-E1/B1 | A/I-H/H-I/A-B2/E2-G/C-B1/E1-F/D
3a: A/I-H/H'-I'/A'-D/F-E2/B2-C/G-E1/B1 | A'/I'-H'/H-I/A-B2/E2-G/C-B1/E1-F/D (AB2CB1,A'D|E1FE2G|HI,H'I')
3b: A/I-H/H-I'/A'-D/F-E2/B2-C/G-E1/B1 | A'/I'-H'/H'-I/A-B2/E2-G/C-B1/E1-F/D (AB2CB1,A'D|E1FE2G|HI'H'I)
3c: A/I-H/H-I/A-D/F-E2/B2-C/G-E1/B1 | A'/I'-H'/H'-I'/A'-B2/E2-G/C-B1/E1-F/D (ADA'B2CB1|E1FE2G|HI,H'I')
3d: A/I-H/H'-I/A-D/F-E2/B2-C/G-E1/B1 | A'/I'-H'/H-I'/A'-B2/E2-G/C-B1/E1-F/D (ADA'B2CB1|E1FE2G|HI'H'I)

Solution 4: A/I-H/H-I/A-B2/E2-E2/B2-B1/E1-E1/B1 (AB2B1|E1,E2|HI)

2|a, 2|b, 2|c: 2
"(8,8,4,6,4,6,4)"

3|a, 2|c: 4
"(4,4,3,5,3,5,3) (0 2)(1)(3 4)(5 6)"

4|a, 2|b, 2|c: 1a
"(8,8,4,6,4,6,4) (5 6)"
4|a, 2|b, 4|c: 1b
"(8,8,4,6,4,6,4) (1)(5 6)"
4|a, 4|b, 2|c: 3a
"(6,6,4,8,4,8,4) [4 6]"
4|a, 4|b, 4|c: 3b
"(12,12,4,8,4,8,4) (1)[4 6]"

6|a, 2|b, 2|c: 1c
"(8,8,6,4,6,4,6) (0 2)(1)(5 6)"
6|a, 2|b, 4|c: 1d
"(8,8,6,4,6,4,6) (0 2)(5 6)"
6|a, 4|b, 2|c: 3c
"(8,8,6,4,6,4,6) (0 2)(1)[4 6]"
6|a, 4|b, 4|c: 3d
"(8,8,6,4,6,4,6) (0 2)[4 6]"

In 7-valent and lower tilings, all splits are in two possibilities, and so each basic solution has a number of sub-solutions that is a power of 2. This does NOT hold in general -- once you get to 8-valent tilings, the kind "AAABAAAB" has some basic solutions where the same edge occurs three or four times. Not ALL permutations of such edges are allowed (basically only transpositions), but it still ups the number of sub-solutions a lot.

The file attached to this post lists "primitive" tilings for up to 6-valent. A primitive tiling is a sort of skeleton that shows which polygons are fundamentally different without regards to whether they have the same number of sides.
As an example, the 5-valent tilings "(3,6,4,6,6) (0 1)(4)", "(3,6,6,6,6) (0 1)(4)", "(4,6,6,6,6) (2 3)(4)", and "(4,6,4,6,6) (0 1)(4)" have the same internal structure (seen from identical Conway symbols) and the same symmetry of a vertex (none), but they can be realized as kinds AAAAB (in two distinct ways), AABAB, or AABAC depending on which polygons are set to have the same amount of sides. But if you would put all three to have the same amount of sides, you would increase the symmetry of the vertex and you'd leave this particular group of tilings.
Attachments
primitive.txt
(9.49 KiB) Downloaded 1 time
Marek14
Pentonian
 
Posts: 1111
Joined: Sat Jul 16, 2005 6:40 pm

Previous

Return to Other Polytopes

Who is online

Users browsing this forum: No registered users and 2 guests

cron