Acronym gabreth Name great birhombitetrahedral honeycomb Confer general polytopal classes: isogonal Externallinks

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
```