Acronym	cabisch
Name	cantic bisnub 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 otch) e.g. would use edges of 3 different sizes: |sefa(s4x)| = w = 1+sqrt(2) = 2.414214, |s3s| = h = sqrt(3) = 1.732051, as well as the here surviving x = 1 (refering to elements of x4s3s4x here).
As a different resizement (x,h,w) → (h,h,q+h) would be possible here.

Incidence matrix according to Dynkin symbol

x4s3s4x   (N → ∞)

demi( . . . . )   | 12N |   2   2   2 |  1  2  1   4  2 | 2  2  2
------------------+-----+-------------+-----------------+--------
demi( x . . . ) & |   2 | 12N   *   * |  1  1  0   1  1 | 1  2  1  x
sefa( x4s . . ) & |   2 |   * 12N   * |  0  1  0   1  1 | 1  1  1  w
sefa( . s3s . )   |   2 |   *   * 12N |  0  0  1   2  0 | 2  0  1  h
------------------+-----+-------------+-----------------+--------
demi( x . . x )   |   4 |   4   0   0 | 3N  *  *   *  * | 2  0  0  x4o
      x4s . .   & |   4 |   2   2   0 |  * 6N  *   *  * | 1  1  0  x w
      . s3s .     |   3 |   0   0   3 |  *  * 4N   *  * | 2  0  0  h3o
sefa( x4s3s . ) & |   4 |   1   1   2 |  *  *  * 12N  * | 1  0  1  xw&#h
sefa( x4s 2 x ) & |   4 |   2   2   0 |  *  *  *   * 6N | 0  1  1  x w
------------------+-----+-------------+-----------------+--------
      x4s3s .   & |  24 |  12  12  24 |  0  6  8  12  0 | N  *  *  pyritohedral sirco-variant xwX Xxw wXx&#zh
      x4s 2 x   & |   8 |   8   4   0 |  2  2  0   0  2 | * 3N  *  long square-prism x4o w
sefa( x4s3s4x )   |   8 |   4   4   4 |  0  0  0   4  2 | *  * 3N  recta xw wx&#h

starting figure: x4x3x4x
where X = w+q = x+2q