xo3od3do3ox&#zh → height = 0
d = 3 (pseudo)
(tegum sum of 2 inverted (x,d)-srips)
o.3o.3o.3o. & | 60 | 2 4 | 1 6 2 | 3 2
------------------+----+--------+-----------+------
x. .. .. .. & | 2 | 60 * | 1 2 0 | 2 1 x
oo3oo3oo3oo&#h | 2 | * 120 | 0 2 1 | 2 1 h
------------------+----+--------+-----------+------
x.3o. .. .. & | 3 | 3 0 | 20 * * | 2 0 x-{3}
xo .. .. ..&#h & | 3 | 1 2 | * 120 * | 1 1 isot
.. od3do ..&#zh | 6 | 0 6 | * * 20 | 2 0 h-{6}
------------------+----+--------+-----------+------
xo3od3do ..&#zh & | 18 | 12 24 | 4 12 4 | 10 * ambo-tut
xo .. .. ox&#h | 4 | 2 4 | 0 4 0 | * 30 disphenoid
xo3oK4Ko3ox&#zk → height = 0
K = kk = 2+sqrt(2) = 3.414214 (pseudo)
k = x(8,2) = sqrt[2+sqrt(2)] = 1.847759
(tegum sum of 2 inverted (x,K)-sricos)
o.3o.4o.3o. & | 576 | 2 4 | 1 6 2 | 3 2
------------------+-----+----------+--------------+-------
x. .. .. .. & | 2 | 576 * | 1 2 0 | 2 1 x
oo3oo4oo3oo&#k | 2 | * 1152 | 0 2 1 | 2 1 h
------------------+-----+----------+--------------+-------
x.3o. .. .. & | 3 | 3 0 | 192 * * | 2 0 x-{3}
xo .. .. ..&#k & | 3 | 1 2 | * 1152 * | 1 1 isot
.. oK4Ko ..&#zk | 8 | 0 8 | * * 144 | 2 0 k-{8}
------------------+-----+----------+--------------+-------
xo3oK4Ko ..&#zk & | 36 | 24 48 | 8 24 6 | 48 * ambo-tic
xo .. .. ox&#k | 4 | 2 4 | 0 4 0 | * 288 disphenoid
uo3ox3xo3ou&#zq → height = 0
u = 2 (pseudo)
(q-laced tegum sum of 2 inverted (u,x)-srips)
o.3o.3o.3o. & | 60 | 4 4 | 2 2 2 6 | 1 3 2
------------------+----+---------+--------------+---------
.. .. x. .. & | 2 | 120 * | 1 1 0 1 | 1 1 1
oo3oo3oo3oo&#q | 2 | * 120 | 0 0 1 2 | 0 2 1
------------------+----+---------+--------------+---------
.. o.3x. .. & | 3 | 3 0 | 40 * * * | 1 0 1 x-{3}
.. .. x.3o. & | 3 | 3 0 | * 40 * * | 1 1 0 x-{3}
uo .. .. ou&#zq | 4 | 0 4 | * * 30 * | 0 2 0 q-{4}
.. ox .. ..&#q & | 3 | 1 2 | * * * 120 | 0 1 1 xqq
------------------+----+---------+--------------+---------
.. o.3x.3o. & | 6 | 12 0 | 4 4 0 0 | 10 * * oct
uo3ox .. ou&#zq & | 9 | 6 12 | 0 2 3 6 | * 20 * rect-trip
.. ox3xo ..&#q | 6 | 6 6 | 2 0 0 6 | * * 20 tall (x,q)-3ap
uo3ox4xo3ou&#zq → height = 0
u = 2 (pseudo)
(q-laced tegum sum of 2 inverted (u,x)-sricos)
o.3o.4o.3o. & | 576 | 4 4 | 2 2 2 6 | 1 3 2
------------------+-----+-----------+------------------+-----------
.. .. x. .. & | 2 | 1152 * | 1 1 0 1 | 1 1 1
oo3oo3oo3oo&#q | 2 | * 1152 | 0 0 1 2 | 0 2 1
------------------+-----+-----------+------------------+-----------
.. o.4x. .. & | 4 | 4 0 | 288 * * * | 1 0 1
.. .. x.3o. & | 3 | 3 0 | * 384 * * | 1 1 0
uo .. .. ou&#zq | 4 | 0 4 | * * 288 * | 0 2 0
.. ox .. ..&#q & | 3 | 1 2 | * * * 1152 | 0 1 1
------------------+-----+-----------+------------------+-----------
.. o.4x.3o. & | 12 | 24 0 | 6 8 0 0 | 48 * * co
uo3ox .. ou&#zq & | 9 | 6 12 | 0 2 3 6 | * 192 * rect-trip
.. ox4xo ..&#q | 8 | 8 8 | 2 0 0 8 | * * 144 tall (x,q)-4ap
oo3xo3ox3oo&#zy → height = 0
y = sqrt(2/5) = 0.632456
(tegum sum of 2 inverted raps)
o.3o.3o.3o. & | 20 | 6 3 | 6 9 | 2 6
-----------------+----+-------+-------+------
.. x. .. .. & | 2 | 60 * | 2 1 | 1 2
oo3oo3oo3oo&#y | 2 | * 30 | 0 4 | 0 4
-----------------+----+-------+-------+------
.. x.3o. .. & | 3 | 3 0 | 40 * | 1 1
.. xo .. ..&#y & | 3 | 1 2 | * 60 | 0 2
-----------------+----+-------+-------+------
.. x.3o.3o. & | 4 | 6 0 | 4 0 | 10 * tet
.. xo3ox ..&#y | 6 | 6 6 | 2 6 | * 20 (x,y)-3ap
oo3xo4ox3oo&#zy → height = 0
y = 2-sqrt(2) = 0.585786
(tegum sum of 2 inverted ricos)
o.3o.4o.3o. & | 192 | 6 3 | 6 9 | 2 6
-----------------+-----+---------+---------+-------
.. x. .. .. & | 2 | 576 * | 2 1 | 1 2
oo3oo4oo3oo&#y | 2 | * 288 | 0 4 | 0 4
-----------------+-----+---------+---------+-------
.. x.4o. .. & | 4 | 4 0 | 288 * | 1 1
.. xo .. ..&#y & | 3 | 1 2 | * 576 | 0 2
-----------------+-----+---------+---------+-------
.. x.4o.3o. & | 8 | 12 0 | 6 0 | 48 * cube
.. xo4ox ..&#y | 8 | 8 8 | 2 8 | * 144 (x,y)-4ap
ao-n-oa bo-m-ob&#zc → height = 0,
a = A*x(2n),
b = B*x(2m),
c = sqrt(A^2+B^2)
(c-laced tegum sum of 2 bidual (a,b)-sized (n,m)-duoprisms)
o.-n-o. o.-m-o. | NM * | 2 2 4 0 0 | 1 1 4 2 4 2 0 0 | 2 2 2 2
.o-n-.o .o-m-.o | * NM | 0 0 4 2 2 | 0 0 2 4 2 4 1 1 | 2 2 2 2
--------------------+-------+-----------------+-------------------------+------------
a. .. .. .. | 2 0 | NM * * * * | 1 0 2 0 0 0 0 0 | 2 1 0 0
.. .. b. .. | 2 0 | * NM * * * | 0 1 0 0 2 0 0 0 | 0 0 1 2
oo-n-oo oo-m-oo&#c | 1 1 | * * 4NM * * | 0 0 1 1 1 1 0 0 | 1 1 1 1
.. .a .. .. | 0 2 | * * * NM * | 0 0 0 2 0 0 1 0 | 2 0 1 0
.. .. .. .b | 0 2 | * * * * NM | 0 0 0 0 0 2 0 1 | 0 1 0 2
--------------------+-------+-----------------+-------------------------+------------
a.-n-o. .. .. | N 0 | N 0 0 0 0 | M * * * * * * * | 2 0 0 0
.. .. b.-m-o. | M 0 | 0 M 0 0 0 | * N * * * * * * | 0 0 0 2
ao .. .. ..&#c | 2 1 | 1 0 2 0 0 | * * 2NM * * * * * | 1 1 0 0
.. oa .. ..&#c | 1 2 | 0 0 2 1 0 | * * * 2NM * * * * | 1 0 1 0
.. .. bo. ..&#c | 2 1 | 0 1 2 0 0 | * * * * 2NM * * * | 0 0 1 1
.. .. .. ob&#c | 1 2 | 0 0 2 0 1 | * * * * * 2NM * * | 0 1 0 1
.o-n-.a .. .. | 0 N | 0 0 0 N 0 | * * * * * * M * | 2 0 0 0
.. .. .o-m-.b | 0 M | 0 0 0 0 M | * * * * * * * N | 0 0 0 2
--------------------+-------+-----------------+-------------------------+------------
ao-n-oa .. ..&#c | N N | N 0 2N N 0 | 1 0 N N 0 0 1 0 | 2M * * * axially scaled n-ap
ao .. .. ob&#c | 2 2 | 1 0 4 0 1 | 0 0 2 0 0 2 0 0 | * NM * * disphenoid
.. oa bo ..&#c | 2 2 | 0 1 4 1 0 | 0 0 0 2 2 0 0 0 | * * NM * disphenoid
.. .. bo-m-ob&#c | M M | 0 M 2M 0 M | 0 1 0 0 M M 0 1 | * * * 2N axially scaled m-ap
s2s3s4s
demi( . . . . ) | 48 | 1 1 1 1 2 2 | 1 1 3 3 3 3 | 1 1 1 1 4
----------------+----+-------------------+-------------------+------------
s2s . . | 2 | 24 * * * * * | 0 0 2 2 0 0 | 1 1 0 0 2
s 2 s . | 2 | * 24 * * * * | 0 0 2 0 2 0 | 1 0 1 0 2
s 2 s | 2 | * * 24 * * * | 0 0 0 2 2 0 | 0 1 1 0 2
. s 2 s | 2 | * * * 24 * * | 0 0 0 2 0 2 | 0 1 0 1 2
sefa( . s3s . ) | 2 | * * * * 48 * | 1 0 1 0 0 1 | 1 0 0 1 1
sefa( . . s4s ) | 2 | * * * * * 48 | 0 1 0 0 1 1 | 0 0 1 1 1
----------------+----+-------------------+-------------------+------------
. s3s . | 3 | 0 0 0 0 3 0 | 16 * * * * * | 1 0 0 1 0
. . s4s | 4 | 0 0 0 0 0 4 | * 12 * * * * | 0 0 1 1 0
sefa( s2s3s . ) | 3 | 1 1 0 0 1 0 | * * 48 * * * | 1 0 0 0 1
sefa( s2s 2 s ) | 3 | 1 0 1 1 0 0 | * * * 48 * * | 0 1 0 0 1
sefa( s 2 s4s ) | 3 | 0 1 1 0 0 1 | * * * * 48 * | 0 0 1 0 1
sefa( . s3s4s ) | 3 | 0 0 0 1 1 1 | * * * * * 48 | 0 0 0 1 1
----------------+----+-------------------+-------------------+------------
s2s3s . | 6 | 3 3 0 0 6 0 | 2 0 6 0 0 0 | 8 * * * *
s2s 2 s | 4 | 2 0 2 2 0 0 | 0 0 0 4 0 0 | * 12 * * *
s 2 s4s | 8 | 0 4 4 0 0 8 | 0 2 0 0 8 0 | * * 6 * *
. s3s4s | 24 | 0 0 0 12 24 24 | 8 6 0 0 0 24 | * * * 2 *
sefa( s2s3s4s ) | 4 | 1 1 1 1 1 1 | 0 0 1 1 1 1 | * * * * 48
s2s3s5s
demi( . . . . ) | 120 | 1 1 1 1 2 2 | 1 1 3 3 3 3 | 1 1 1 1 4
----------------+-----+---------------------+-----------------------+---------------
s2s . . | 2 | 60 * * * * * | 0 0 2 2 0 0 | 1 1 0 0 2
s 2 s . | 2 | * 60 * * * * | 0 0 2 0 2 0 | 1 0 1 0 2
s 2 s | 2 | * * 60 * * * | 0 0 0 2 2 0 | 0 1 1 0 2
. s 2 s | 2 | * * * 60 * * | 0 0 0 2 0 2 | 0 1 0 1 2
sefa( . s3s . ) | 2 | * * * * 120 * | 1 0 1 0 0 1 | 1 0 0 1 1
sefa( . . s5s ) | 2 | * * * * * 120 | 0 1 0 0 1 1 | 0 0 1 1 1
----------------+-----+---------------------+-----------------------+---------------
. s3s . | 3 | 0 0 0 0 3 0 | 40 * * * * * | 1 0 0 1 0
. . s5s | 5 | 0 0 0 0 0 5 | * 24 * * * * | 0 0 1 1 0
sefa( s2s3s . ) | 3 | 1 1 0 0 1 0 | * * 120 * * * | 1 0 0 0 1
sefa( s2s 2 s ) | 3 | 1 0 1 1 0 0 | * * * 120 * * | 0 1 0 0 1
sefa( s 2 s5s ) | 3 | 0 1 1 0 0 1 | * * * * 120 * | 0 0 1 0 1
sefa( . s3s5s ) | 3 | 0 0 0 1 1 1 | * * * * * 120 | 0 0 0 1 1
----------------+-----+---------------------+-----------------------+---------------
s2s3s . | 6 | 3 3 0 0 6 0 | 2 0 6 0 0 0 | 20 * * * *
s2s 2 s | 4 | 2 0 2 2 0 0 | 0 0 0 4 0 0 | * 30 * * *
s 2 s5s | 10 | 0 5 5 0 0 10 | 0 2 0 0 10 0 | * * 12 * *
. s3s5s | 60 | 0 0 0 30 60 60 | 20 12 0 0 0 60 | * * * 2 *
sefa( s2s3s5s ) | 4 | 1 1 1 1 1 1 | 0 0 1 1 1 1 | * * * * 120
1200 | 1 2 1 1 1 | 3 2 2 1 3 | 5 1 1
-----+----------------------+----------------------+------------
2 | 600 * * * * | 0 2 0 0 3 | 5 0 0 a, eg. x
2 | * 1200 * * * | 1 0 1 1 1 | 2 1 1 b1, eg. x
2 | * * 600 * * | 2 0 0 0 1 | 2 1 0 b2, eg. x
2 | * * * 600 * | 2 1 0 0 0 | 2 1 0 b3, eg. x
2 | * * * * 600 | 0 1 2 0 0 | 2 0 1 c, eg. u
-----+----------------------+----------------------+------------
3 | 0 1 1 1 0 | 1200 * * * * | 1 1 0 b3o = b1,b2,b3
4 | 2 0 0 1 1 | * 600 * * * | 2 0 0 bc&#a = a,b3,a,c
4 | 0 2 0 0 2 | * * 600 * * | 1 0 1 b2c = b1,c,b1,c
5 | 0 5 0 0 0 | * * * 240 * | 0 1 1 b5o = b1,b1,b1,b1,b1
6 | 3 2 1 0 0 | * * * * 600 | 2 0 0 a3b = a,b1,a,b1,a,b2
-----+----------------------+----------------------+------------
10 | 5 4 2 2 2 | 2 2 1 0 2 | 600 * * shaved tut
10 | 0 10 5 5 0 | 10 0 0 2 0 | * 120 * pap
10 | 0 10 0 0 5 | 0 0 5 2 0 | * * 120 pip
72 | 2 2 4 | 1 6 4 2 | 3 2 2
---+-----------+--------------+---------
2 | 72 * * | 1 2 0 0 | 2 1 0 x
2 | * 72 * | 0 2 2 0 | 2 1 1 x
2 | * * 144 | 0 1 1 1 | 1 1 1 q
---+-----------+--------------+---------
3 | 3 0 0 | 24 * * * | 2 0 0 xxx
3 | 1 1 1 | * 144 * * | 1 1 0 xxq
4 | 0 2 2 | * * 72 * | 1 0 1 xqxq
3 | 0 0 3 | * * * 48 | 0 1 1 qqq
---+-----------+--------------+---------
9 | 6 6 6 | 2 6 3 0 | 24 * * chiral tridim. co
6 | 3 3 6 | 0 6 0 2 | * 24 * qo3oq&#x
6 | 0 3 6 | 0 0 3 2 | * * 24 x q3o
xo3yb3by3ox&#zh → height = 0
y > 0 (depending on truncation depth)
b = y+3
(h-laced tegum sum of 2 inverted (x,y,b)-grips)
o.3o.3o.3o. & | 120 | 1 1 2 | 1 3 2 | 3 1
------------------+-----+-----------+-----------+------
x. .. .. .. & | 2 | 60 * * | 1 2 0 | 2 1 x
.. y. .. .. & | 2 | * 60 * | 1 0 2 | 3 0 y
oo3oo3oo3oo&#h | 2 | * * 120 | 0 2 1 | 2 1 h
------------------+-----+-----------+-----------+------
x.3y. .. .. & | 6 | 3 3 0 | 20 * * | 2 0 (x,y)-{6}
xo .. .. ..&#h & | 3 | 1 0 2 | * 120 * | 1 1 xhh
.. yb3by ..&#zh | 12 | 0 6 6 | * * 20 | 2 0 (y,h)-{12}
------------------+-----+-----------+-----------+------
xo3yb3by ..&#zh & | 36 | 12 18 24 | 4 12 4 | 10 * trunc-tut
xo .. .. ox&#h | 4 | 2 0 4 | 0 4 0 | * 30 disphenoid
xo3yb4by3ox&#zk → height = 0
k = x(8,2) = sqrt[2+sqrt(2)] = 1.847759
y > 0 (depending on truncation depth)
b = y+2+sqrt(2) (pseudo)
(k-laced tegum sum of 2 inverted (x,y,b)-gricoes)
o.3o.4o.3o. & | 1152 | 1 1 2 | 1 3 2 | 3 1
------------------+------+--------------+--------------+-------
x. .. .. .. & | 2 | 576 * * | 1 2 0 | 2 1 x
.. y. .. .. & | 2 | * 576 * | 1 0 2 | 3 0 y
oo3oo4oo3oo&#k | 2 | * * 1152 | 0 2 1 | 2 1 k
------------------+------+--------------+--------------+-------
x.3y. .. .. & | 6 | 3 3 0 | 192 * * | 2 0 (x,y)-{6}
xo .. .. ..&#k & | 3 | 1 0 2 | * 1152 * | 1 1 xkk
.. yb4by ..&#zk | 16 | 0 8 8 | * * 144 | 2 0 (y,k)-{16}
------------------+------+--------------+--------------+-------
xo3yb4by ..&#zk & | 72 | 24 36 48 | 8 24 6 | 48 * trunc-tic
xo .. .. ox&#k | 4 | 2 0 4 | 0 4 0 | * 288 disphenoid
by3ox3xo3yb&#zq → height = 0
y > 0 (depending on truncation depth)
b = y+2 (pseudo)
(q-laced tegum sum of 2 inverted (b,x,y)-prips)
o.3o.3o.3o. & | 120 | 2 1 2 | 1 2 2 3 | 1 3 1
------------------+-----+------------+--------------+---------
.. .. x. .. & | 2 | 120 * * | 1 1 0 1 | 1 1 1 x
.. .. .. y. & | 2 | * 60 * | 0 2 2 0 | 1 3 0 y
oo3oo3oo3oo&#q | 2 | * * 120 | 0 0 1 2 | 0 2 1 q
------------------+-----+------------+--------------+---------
.. o.3x. .. & | 3 | 3 0 0 | 40 * * * | 1 0 1 x-{3}
.. .. x.3y. & | 6 | 3 3 0 | * 40 * * | 1 1 0 (x,y)-{6}
by .. .. yb&#zq | 8 | 0 4 4 | * * 30 * | 0 2 0 (y,q)-{8}
.. ox .. ..&#q & | 3 | 1 0 2 | * * * 120 | 0 1 1 xqq
------------------+-----+------------+--------------+---------
.. o.3x.3y. & | 12 | 12 6 0 | 4 4 0 0 | 10 * * (x,y)-tut
by3ox .. yb&#zq & | 18 | 6 9 12 | 0 2 3 6 | * 20 * trunc-trip
.. ox3xo ..&#q | 6 | 6 0 6 | 2 0 0 6 | * * 20 tall (x,q)-3ap
by3ox4xo3yb&#zq → height = 0
y > 0 (depending on truncation depth)
b = y+2 (pseudo)
(q-laced tegum sum of 2 inverted (b,x,y)-pricos)
o.3o.4o.3o. & | 1152 | 2 1 2 | 1 2 2 3 | 1 3 1
------------------+------+---------------+------------------+-----------
.. .. x. .. & | 2 | 1152 * * | 1 1 0 1 | 1 1 1 x
.. .. .. y. & | 2 | * 576 * | 0 2 2 0 | 1 3 0 y
oo3oo4oo3oo&#q | 2 | * * 1152 | 0 0 1 2 | 0 2 1 q
------------------+------+---------------+------------------+-----------
.. o.4x. .. & | 4 | 4 0 0 | 288 * * * | 1 0 1 x-{3}
.. .. x.3y. & | 6 | 3 3 0 | * 384 * * | 1 1 0 (x,y)-{6}
by .. .. yb&#zq | 8 | 0 4 4 | * * 288 * | 0 2 0 (y,q)-{8}
.. ox .. ..&#q & | 3 | 1 0 2 | * * * 1152 | 0 1 1 xqq
------------------+------+---------------+------------------+-----------
.. o.4x.3y. & | 24 | 24 12 0 | 6 8 0 0 | 48 * * (x,y)-toe
by3ox .. yb&#zq & | 18 | 6 9 12 | 0 2 3 6 | * 192 * trunc-trip
.. ox4xo ..&#q | 8 | 8 0 8 | 2 0 0 8 | * * 144 (x,q)-squap
xo3xo3ox3ox&#zc - height = 0
c = sqrt(7/5)
o.3o.3o.3o. & | 40 | 1 3 6 | 3 9 9 | 1 6 3 3
------------------+----+-----------+------------+------------
x. .. .. .. & | 2 | 20 * * | 0 6 0 | 3 3 0 0 x
.. x. .. .. & | 2 | * 60 * | 2 0 2 | 1 1 0 2 y
oo3oo3oo3oo&#c | 2 | * * 120 | 0 2 2 | 0 2 1 1 c
------------------+----+-----------+------------+------------
.. x.3o. .. & | 3 | 0 3 0 | 40 * * | 1 0 0 1 x-{3}
xo .. .. ..&#c & | 3 | 1 0 2 | * 120 * | 0 1 1 0 xcc
.. xo .. ..&#c & | 3 | 0 1 2 | * * 120 | 0 1 0 1 xcc
------------------+----+-----------+------------+------------
.. x.3o.3o. & | 4 | 0 6 0 | 4 0 0 | 10 * * * x-tet
xo .. ox ..&#c & | 4 | 1 1 4 | 0 2 2 | * 60 * * tall (x,c)-2ap
xo .. .. ox&#c | 4 | 2 0 4 | 0 4 0 | * * 30 * tall (x,c)-2ap
.. xo3ox ..&#c & | 6 | 0 6 6 | 2 0 6 | * * * 20 tall (x,c)-3ap
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