©in doubled symmetry as o4s3s4o as s3s3s *b4o as s3s3s3s3*a
- general polytopal classes:
- isogonal
links
| 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 cannot be made uniform:The merealternated faceting (here starting atbatch) 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 toDynkin 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 2sefa( . s3s . ) | 2 | * * 24N | 1 1 1 | 1 1 1----------------+----+-----------+------------+------- . s3s . | 3 | 0 0 3 | 8N * * | 1 1 0sefa( o4s3s . ) | 3 | 1 0 2 | * 12N * | 1 0 1sefa( . 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
ordemi( . . . . ) |3N | 2 8 | 4 12 | 4 4------------------+----+--------+--------+----- o4s . . & | 2 | 3N * | 0 4 | 2 2sefa( . s3s . ) | 2 | * 12N | 1 2 | 2 1------------------+----+--------+--------+----- . s3s . | 3 | 0 3 | 4N * | 2 0sefa( o4s3s . ) & | 3 | 1 2 | * 12N | 1 1------------------+----+--------+--------+----- o4s3s . &♦ 12 | 6 24 | 8 12 | N *sefa( o4s3s4o )♦ 4 | 2 4 | 0 4 | * 3Nstarting 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 2sefa( s3s . . ) | 2 | * * 24N * | 1 0 1 1 0 | 1 1 0 1sefa( . 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 0sefa( s3s3s . ) | 3 | 1 0 1 1 | * * 24N * * | 1 0 0 1sefa( s3s . *b4o ) | 3 | 0 1 2 0 | * * * 12N * | 0 1 0 1sefa( . 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 | * * * 12Nstarting 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 2sefa( s3s . . ) | 2 | * * 12N * * * | 1 0 0 0 1 1 0 0 | 1 1 0 0 1sefa( s . . s3*a ) | 2 | * * * 12N * * | 0 1 0 0 0 1 1 0 | 0 1 1 0 1sefa( . s3s . ) | 2 | * * * * 12N * | 0 0 1 0 1 0 0 1 | 1 0 0 1 1sefa( . . 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 0sefa( s3s3s . ) | 3 | 1 0 1 0 1 0 | * * * * 12N * * * | 1 0 0 0 1sefa( s3s . s3*a ) | 3 | 0 1 1 1 0 0 | * * * * * 12N * * | 0 1 0 0 1sefa( s . s3s3*a ) | 3 | 1 0 0 1 0 1 | * * * * * * 12N * | 0 0 1 0 1sefa( . 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 | * * * * 12Nstarting figure:x3x3x3x3*a
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