## Hyperbolic Tilings

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

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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.

wendy
Pentonian

Posts: 1814
Joined: Tue Jan 18, 2005 12:42 pm
Location: Brisbane, Australia

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

AAAAAAB example: three distinct 3,3,3,3,3,3,3A colorings
Attachments
3_7_57b.png
3_7_60d.png
3_7_75b.png
Marek14
Pentonian

Posts: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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: 1101
Joined: Sat Jul 16, 2005 6:40 pm

### Re: Hyperbolic Tilings

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
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