Acronym | snich, s4s3s4s |
Name |
(full) snub cubical honeycomb, snub bicubic honeycomb |
External links |
Although all cells individually have uniform realisations, the honeycomb as a total can not be made uniform: The mere alternated faceting (here starting at otch) e.g. would use edges of 3 different sizes: |sefa(s4s)| = x(8) = sqrt[2+sqrt(2)] = 1.847759, |s2s| = x(4) = sqrt(2) = 1.414214, and |sefa(s3s)| = x(6) = sqrt(3) = 1.732051 (refering to elements of s4s3s4s here).
Incidence matrix according to Dynkin symbol
s4s3s4s (N → ∞) demi( . . . . ) | 24N | 1 1 1 2 2 2 | 1 1 1 3 3 3 3 | 1 1 1 1 4 ----------------+-----+-------------------------+--------------------------+-------------- s 2 s . | 2 | 12N * * * * * | 0 0 0 2 0 2 0 | 1 0 1 0 2 s . 2 s | 2 | * 12N * * * * | 0 0 0 0 2 2 0 | 0 1 1 0 2 . s 2 s | 2 | * * 12N * * * | 0 0 0 0 2 0 2 | 0 1 0 1 2 sefa( s4s . . ) | 2 | * * * 24N * * | 1 0 0 1 1 0 0 | 1 1 0 0 1 sefa( . s3s . ) | 2 | * * * * 24N * | 0 1 0 1 0 0 1 | 1 0 0 1 1 sefa( . . s4s ) | 2 | * * * * * 24N | 0 0 1 0 0 1 1 | 0 0 1 1 1 ----------------+-----+-------------------------+--------------------------+-------------- s4s . . | 4 | 0 0 0 4 0 0 | 6N * * * * * * | 1 1 0 0 0 . s3s . | 3 | 0 0 0 0 3 0 | * 8N * * * * * | 1 0 0 1 0 . . s4s | 4 | 0 0 0 0 0 4 | * * 6N * * * * | 0 0 1 1 0 sefa( s4s3s . ) | 3 | 1 0 0 1 1 0 | * * * 24N * * * | 1 0 0 0 1 sefa( s4s 2 s ) | 3 | 0 1 1 1 0 0 | * * * * 24N * * | 0 1 0 0 1 sefa( s 2 s4s ) | 3 | 1 1 0 0 0 1 | * * * * * 24N * | 0 0 1 0 1 sefa( . s3s4s ) | 3 | 0 0 1 0 1 1 | * * * * * * 24N | 0 0 0 1 1 ----------------+-----+-------------------------+--------------------------+-------------- s4s3s . ♦ 24 | 12 0 0 24 24 0 | 6 8 0 24 0 0 0 | N * * * * s4s 2 s ♦ 8 | 0 4 4 8 0 0 | 2 0 0 0 8 0 0 | * 3N * * * s 2 s4s ♦ 8 | 4 4 0 0 0 8 | 0 0 2 0 0 8 0 | * * 3N * * . s3s4s ♦ 24 | 0 0 12 0 24 24 | 0 8 6 0 0 0 24 | * * * N * sefa( s4s3s4s ) ♦ 4 | 1 1 1 1 1 1 | 0 0 0 1 1 1 1 | * * * * 24N
or demi( . . . . ) | 12N | 2 1 4 2 | 2 1 6 6 | 2 2 4 ------------------+-----+----------------+---------------+--------- s 2 s . & | 2 | 12N * * * | 0 0 2 2 | 1 1 2 s . 2 s | 2 | * 6N * * | 0 0 0 4 | 0 2 2 sefa( s4s . . ) & | 2 | * * 24N * | 1 0 1 1 | 1 1 1 sefa( . s3s . ) | 2 | * * * 12N | 0 1 2 0 | 2 0 1 ------------------+-----+----------------+---------------+--------- s4s . . & | 4 | 0 0 4 0 | 6N * * * | 1 1 0 . s3s . | 3 | 0 0 0 3 | * 4N * * | 2 0 0 sefa( s4s3s . ) & | 3 | 1 0 1 1 | * * 24N * | 1 0 1 sefa( s4s 2 s ) | 3 | 1 1 1 0 | * * * 24N | 0 1 1 ------------------+-----+----------------+---------------+--------- s4s3s . & ♦ 24 | 12 0 24 24 | 6 8 24 0 | N * * s4s 2 s & ♦ 8 | 4 4 8 0 | 2 0 0 8 | * 3N * sefa( s4s3s4s ) ♦ 4 | 2 1 2 1 | 0 0 2 2 | * * 12N starting figure: x4x3x4x
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