Acronym | gabreth |
Name | great birhombitetrahedral honeycomb |
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 otch)
e.g. would use edges of 3 different sizes:
|sefa(s4x)| = w = 1+sqrt(2) = 2.414214, |s2s| = q = sqrt(2) = 1.414214, as well as the here surviving
x = 1 (refering to elements of s4x3x4s here).
As a different resizement (x,q,w) → (x,x,u) would be possible here.
Incidence matrix according to Dynkin symbol
s4x3x4s (N → ∞) demi( . . . . ) | 12N | 2 1 2 | 1 2 2 4 | 2 2 2 ------------------+-----+------------+--------------+-------- demi( . x . . ) & | 2 | 12N * * | 1 1 1 1 | 2 1 1 x s 2 s | 2 | * 6N * | 0 0 0 4 | 0 2 2 q sefa( s4x . . ) & | 2 | * * 12N | 0 1 1 1 | 1 1 1 w ------------------+-----+------------+--------------+-------- demi( . x3x . ) | 6 | 6 0 0 | 2N * * * | 2 0 0 x3x s4x . . & | 4 | 2 0 2 | * 6N * * | 1 1 0 x2w sefa( s4x3x . ) & | 6 | 3 0 3 | * * 4N * | 1 0 1 x3w sefa( s4x 2 s ) & | 4 | 1 2 1 | * * * 12N | 0 1 1 xw&#q ------------------+-----+------------+--------------+-------- s4x3x . & | 24 | 24 0 12 | 4 6 4 0 | N * * x3x3w (toe variant) s4x 2 s & | 8 | 4 4 4 | 0 2 0 4 | * 3N * xw2wx&#q (recta) sefa( s4x3x4s ) | 12 | 6 6 6 | 0 0 2 6 | * * 2N xw3wx&#q (ditra) starting figure: x4x3x4x
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