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| Acronym | serch |
| Name | snub rectified cubic honeycomb |
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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 grich) e.g. would use edges of 3 different sizes: |sefa(s4s)| = x(8) = sqrt[2+sqrt(2)] = 1.847759, |s2s| = |s4o| = x(4) = sqrt(2) = 1.414214, and |sefa(s3s)| = x(6) = sqrt(3) = 1.732051 (refering to elements of s4s3s4o here). – But one might e.g. resize it in such a way that all snics would become uniform. That is, we would get |sefa(s4s)| = |sefa(s3s)| = |s2s| = 1. Then the remaining edge type s4o, as can be seen from the above picture, would become twice the distance between the nearest vertex of the twisted squares to the tangent plane of the neighbouring square (of that snic), i.e. resulting in 2(C3-C2)=1.042768 (for the numbers Ck cf. to snic). I.e. the ikes then will remain pyritohedral: This honeycomb therefore qualifies as a near miss (with some edges then being about 4% too long).
Incidence matrix according to Dynkin symbol
s4s3s4o (N → ∞)
demi( . . . . ) | 12N | 2 1 2 4 | 1 2 6 3 3 | 2 1 1 4
----------------+-----+----------------+-------------------+-----------
s 2 s . | 2 | 12N * * * | 0 0 2 2 0 | 1 1 0 2
. . s4o | 2 | * 6N * * | 0 0 0 2 2 | 0 1 1 2
sefa( s4s . . ) | 2 | * * 12N * | 1 0 2 0 0 | 2 0 0 1
sefa( . s3s . ) | 2 | * * * 24N | 0 1 1 0 1 | 1 0 1 1
----------------+-----+----------------+-------------------+-----------
s4s . . | 4 | 0 0 4 0 | 3N * * * * | 2 0 0 0
. s3s . | 3 | 0 0 0 3 | * 8N * * * | 1 0 1 0
sefa( s4s3s . ) | 3 | 1 0 1 1 | * * 24N * * | 1 0 0 1
sefa( s 2 s4o ) | 3 | 2 1 0 0 | * * * 12N * | 0 1 0 1
sefa( . s3s4o ) | 3 | 0 1 0 2 | * * * * 12N | 0 0 1 1
----------------+-----+----------------+-------------------+-----------
s4s3s . ♦ 24 | 12 0 24 24 | 6 8 24 0 0 | N * * *
s 2 s4o ♦ 4 | 4 2 0 0 | 0 0 0 4 0 | * 3N * *
. s3s4o ♦ 12 | 0 6 0 24 | 0 8 0 0 12 | * * N *
sefa( s4s3s4o ) ♦ 4 | 2 1 1 2 | 0 0 2 1 1 | * * * 12N
starting figure: x4x3x4o
s3s3s *b4s (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 0 2 2 | 0 0 1 1 2
sefa( s3s . . ) | 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( . s . *b4s ) | 2 | * * * * * 24N | 0 0 1 0 1 0 1 | 0 1 0 1 1
-------------------+-----+-------------------------+--------------------------+--------------
s3s . . | 3 | 0 0 0 3 0 0 | 8N * * * * * * | 1 1 0 0 0
. s3s . | 3 | 0 0 0 0 3 0 | * 8N * * * * * | 1 0 0 1 0
. s . *b4s | 4 | 0 0 0 0 0 4 | * * 6N * * * * | 0 1 0 1 0
sefa( s3s3s . ) | 3 | 1 0 0 1 1 0 | * * * 24N * * * | 1 0 0 0 1
sefa( s3s . *b4s ) | 3 | 0 1 0 1 0 1 | * * * * 24N * * | 0 1 0 0 1
sefa( s 2 s 2 s ) | 3 | 1 1 1 0 0 0 | * * * * * 24N * | 0 0 1 0 1
sefa( . s3s *b4s ) | 3 | 0 0 1 0 1 1 | * * * * * * 24N | 0 0 0 1 1
-------------------+-----+-------------------------+--------------------------+--------------
s3s3s . ♦ 12 | 6 0 0 12 12 0 | 4 4 0 12 0 0 0 | 2N * * * *
s3s . *b4s ♦ 24 | 0 12 0 24 0 24 | 8 0 6 0 24 0 0 | * N * * *
s 2 s 2 s ♦ 4 | 2 2 2 0 0 0 | 0 0 0 0 0 4 0 | * * 6N * *
. s3s *b4s ♦ 24 | 0 0 12 0 24 24 | 0 8 6 0 0 0 24 | * * * N *
sefa( s3s3s *b4s ) ♦ 4 | 1 1 1 1 1 1 | 0 0 0 1 1 1 1 | * * * * 24N
starting figure: x3x3x *b4x
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