Acronym | esch |
Name | edge-snub cubic honeycomb |
Confer |
|
External links |
Although all cells individually have uniform realisations, the honeycomb as a total can not be made uniform: The mere edge-alternated faceting (here starting at giddich) e.g. would use edges of 5 different sizes: |s4s| = k = sqrt[2+sqrt(2)] = 1.847759, |s2s| = q = sqrt(2) = 1.414214, |s3s| = h = sqrt(3) = 1.732051, |sefa(x4s)| = w = 1+sqrt(2) = 2.414214, as well as the here surviving x = 1 (refering to elements of s4s3s4x here).
Incidence matrix according to Dynkin symbol
s4s3s4x (N → ∞) demi( . . . . ) | 24N | 1 1 2 2 1 | 1 1 1 3 2 2 2 | 1 1 1 1 3 ----------------+-----+---------------------+--------------------------+-------------- demi( . . . x ) | 2 | 12N * * * * | 0 0 1 0 2 1 1 | 0 1 1 1 2 x s 2 s . | 2 | * 12N * * * | 0 0 0 2 0 2 0 | 1 0 1 0 2 q sefa( s4s . . ) | 2 | * * 24N * * | 1 0 0 1 1 0 0 | 1 1 0 0 1 k sefa( . s3s . ) | 2 | * * * 24N * | 0 1 0 1 0 0 1 | 1 0 0 1 1 h sefa( . . s4x ) | 2 | * * * * 12N | 0 0 1 0 0 1 1 | 0 0 1 1 1 w ----------------+-----+---------------------+--------------------------+-------------- s4s . . | 4 | 0 0 4 0 0 | 6N * * * * * * | 1 1 0 0 0 k4o . s3s . | 3 | 0 0 0 3 0 | * 8N * * * * * | 1 0 0 1 0 h3o . . s4x | 4 | 2 0 0 0 2 | * * 6N * * * * | 0 0 1 1 0 x w sefa( s4s3s . ) | 3 | 0 1 1 1 0 | * * * 24N * * * | 1 0 0 0 1 (q,h,k)-{3} sefa( s4s 2 x ) | 4 | 2 0 2 0 0 | * * * * 12N * * | 0 1 0 0 1 x k sefa( s 2 s4x ) | 4 | 1 2 0 0 1 | * * * * * 12N * | 0 0 1 0 1 xw&#q sefa( . s3s4x ) | 4 | 1 0 0 2 1 | * * * * * * 12N | 0 0 0 1 1 xw&#h ----------------+-----+---------------------+--------------------------+-------------- s4s3s . | 24 | 0 12 24 24 0 | 6 8 0 24 0 0 0 | N * * * * snic variant s4s 2 x | 8 | 4 0 8 0 0 | 2 0 0 0 4 0 0 | * 3N * * * (k,x)-4p s 2 s4x | 8 | 4 4 0 0 4 | 0 0 2 0 0 4 0 | * * 3N * * xw wx&#q recta . s3s4x | 24 | 12 0 0 24 12 | 0 8 6 0 0 0 12 | * * * N * pyritohedral sirco variant sefa( s4s3s4x ) | 6 | 2 2 2 2 1 | 0 0 0 2 1 1 1 | * * * * 12N wx2ox&#(q,h) slanted wedge (trip variant)
© 2004-2024 | top of page |