© in doubled symmetry as o4s3s4o as s3s3s *b4o as s3s3s3s3*a
- general polytopal classes:
- isogonal
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| Acronym | bisch |
| Name | bisnub cubic honeycomb |
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| Confer |
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Although all cells individually have uniform realisations, the honeycomb as a total can not be made uniform: The mere alternated faceting (here starting at batch) e.g. would use edges of 2 different sizes: |s4o| = x(4) = sqrt(2) = 1.414214 and |sefa(s3s)| = x(6) = sqrt(3) = 1.732051 (refering to elements of o4s3s4o here).
Incidence matrix according to Dynkin symbol
o4s3s4o (N → ∞)
demi( . . . . ) | 6N | 1 1 8 | 4 6 6 | 2 2 4
----------------+----+-----------+------------+-------
o4s . . | 2 | 3N * * | 0 4 0 | 2 0 2
. . s4o | 2 | * 3N * | 0 0 4 | 0 2 2
sefa( . s3s . ) | 2 | * * 24N | 1 1 1 | 1 1 1
----------------+----+-----------+------------+-------
. s3s . | 3 | 0 0 3 | 8N * * | 1 1 0
sefa( o4s3s . ) | 3 | 1 0 2 | * 12N * | 1 0 1
sefa( . s3s4o ) | 3 | 0 1 2 | * * 12N | 0 1 1
----------------+----+-----------+------------+-------
o4s3s . ♦ 12 | 6 0 24 | 8 12 0 | N * *
. s3s4o ♦ 12 | 0 6 24 | 8 0 12 | * N *
sefa( o4s3s4o ) ♦ 4 | 1 1 4 | 0 2 2 | * * 6N
or
demi( . . . . ) | 3N | 2 8 | 4 12 | 4 4
------------------+----+--------+--------+-----
o4s . . & | 2 | 3N * | 0 4 | 2 2
sefa( . s3s . ) | 2 | * 12N | 1 2 | 2 1
------------------+----+--------+--------+-----
. s3s . | 3 | 0 3 | 4N * | 2 0
sefa( o4s3s . ) & | 3 | 1 2 | * 12N | 1 1
------------------+----+--------+--------+-----
o4s3s . & ♦ 12 | 6 24 | 8 12 | N *
sefa( o4s3s4o ) ♦ 4 | 2 4 | 0 4 | * 3N
starting figure: o4x3x4o
s3s3s *b4o (N → ∞)
demi( . . . . ) | 12N | 1 1 4 4 | 2 2 6 3 3 | 2 1 1 4
-------------------+-----+---------------+-------------------+-----------
s 2 s . | 2 | 6N * * * | 0 0 4 0 0 | 2 0 0 2
. s . *b4o | 2 | * 6N * * | 0 0 0 2 2 | 0 1 1 2
sefa( s3s . . ) | 2 | * * 24N * | 1 0 1 1 0 | 1 1 0 1
sefa( . s3s . ) | 2 | * * * 24N | 0 1 1 0 1 | 1 0 1 1
-------------------+-----+---------------+-------------------+-----------
s3s . . | 3 | 0 0 3 0 | 8N * * * * | 1 1 0 0
. s3s . | 3 | 0 0 0 3 | * 8N * * * | 1 0 1 0
sefa( s3s3s . ) | 3 | 1 0 1 1 | * * 24N * * | 1 0 0 1
sefa( s3s . *b4o ) | 3 | 0 1 2 0 | * * * 12N * | 0 1 0 1
sefa( . s3s *b4o ) | 3 | 0 1 0 2 | * * * * 12N | 0 0 1 1
-------------------+-----+---------------+-------------------+-----------
s3s3s . ♦ 12 | 6 0 12 12 | 4 4 12 0 0 | 2N * * *
s3s . *b4o ♦ 12 | 0 6 24 0 | 8 0 0 12 0 | * N * *
. s3s *b4o ♦ 12 | 0 6 0 24 | 0 8 0 0 12 | * * N *
sefa( s3s3s *b4o ) ♦ 4 | 1 1 2 2 | 0 0 2 1 1 | * * * 12N
starting figure: x3x3x *b4o
s3s3s3s3*a (N → ∞)
demi( . . . . ) | 12N | 1 1 2 2 2 2 | 1 1 1 1 3 3 3 3 | 1 1 1 1 4
-------------------+-----+-----------------------+-----------------------------+------------
s 2 s . | 2 | 6N * * * * * | 0 0 0 0 2 0 2 0 | 1 0 1 0 2
. s 2 s | 2 | * 6N * * * * | 0 0 0 0 0 2 0 2 | 0 1 0 1 2
sefa( s3s . . ) | 2 | * * 12N * * * | 1 0 0 0 1 1 0 0 | 1 1 0 0 1
sefa( s . . s3*a ) | 2 | * * * 12N * * | 0 1 0 0 0 1 1 0 | 0 1 1 0 1
sefa( . s3s . ) | 2 | * * * * 12N * | 0 0 1 0 1 0 0 1 | 1 0 0 1 1
sefa( . . s3s ) | 2 | * * * * * 12N | 0 0 0 1 0 0 1 1 | 0 0 1 1 1
-------------------+-----+-----------------------+-----------------------------+------------
s3s . . | 3 | 0 0 3 0 0 0 | 4N * * * * * * * | 1 1 0 0 0
s . . s3*a | 3 | 0 0 0 3 0 0 | * 4N * * * * * * | 0 1 1 0 0
. s3s . | 3 | 0 0 0 0 3 0 | * * 4N * * * * * | 1 0 0 1 0
. . s3s | 3 | 0 0 0 0 0 3 | * * * 4N * * * * | 0 0 1 1 0
sefa( s3s3s . ) | 3 | 1 0 1 0 1 0 | * * * * 12N * * * | 1 0 0 0 1
sefa( s3s . s3*a ) | 3 | 0 1 1 1 0 0 | * * * * * 12N * * | 0 1 0 0 1
sefa( s . s3s3*a ) | 3 | 1 0 0 1 0 1 | * * * * * * 12N * | 0 0 1 0 1
sefa( . s3s3s ) | 3 | 0 1 0 0 1 1 | * * * * * * * 12N | 0 0 0 1 1
-------------------+-----+-----------------------+-----------------------------+------------
s3s3s . ♦ 12 | 6 0 12 0 12 0 | 4 0 4 0 12 0 0 0 | N * * * *
s3s . s3*a ♦ 12 | 0 6 12 12 0 0 | 4 4 0 0 0 12 0 0 | * N * * *
s . s3s3*a ♦ 12 | 6 0 0 12 0 12 | 0 4 0 4 0 0 12 0 | * * N * *
. s3s3s ♦ 12 | 0 6 0 0 12 12 | 0 0 4 4 0 0 0 12 | * * * N *
sefa( s3s3s3s3*a ) ♦ 4 | 1 1 1 1 1 1 | 0 0 0 0 1 1 1 1 | * * * * 12N
starting figure: x3x3x3x3*a
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