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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