Acronym	rusch
Name	runcicantic snub cubic honeycomb
Confer	general polytopal classes: isogonal
External links

Although all cells individually have uniform realisations, the honeycomb as a total can not be made uniform: The mere face-alternated faceting (here starting at prich) e.g. would use edges of 3 different sizes: |s2s| = |s4o| = q = sqrt(2) = 1.414214, |sefa(x4s)| = w = 1+sqrt(2) = 2.414214, as well as the here surviving x = 1 (refering to elements of s4x3o4s here).

Incidence matrix according to Dynkin symbol

s4x3o4s   (N → ∞)

demi( . . . . ) | 12N |   2   2  1   2 |  1  2  1   4   3  2 | 1  2  1 1  3
----------------+-----+----------------+---------------------+-------------
demi( . x . . ) |   2 | 12N   *  *   * |  1  1  0   1   0  1 | 1  1  0 1  1  x
      s  2  s   |   2 |   * 12N  *   * |  0  0  0   2   2  0 | 0  1  1 0  2  q
      . . o4s   |   2 |   *   * 6N   * |  0  0  0   0   2  2 | 0  0  1 1  2  q
sefa( s4x . . ) |   2 |   *   *  * 12N |  0  1  1   1   0  0 | 1  1  0 0  1  w
----------------+-----+----------------+---------------------+-------------
demi( . x3o . ) |   3 |   3   0  0   0 | 4N  *  *   *   *  * | 1  0  0 1  0  x3o
      s4x . .   |   4 |   2   0  0   2 |  * 6N  *   *   *  * | 1  1  0 0  0  x w
sefa( s4x3o . ) |   3 |   0   0  0   3 |  *  * 4N   *   *  * | 1  0  0 0  1  w3o
sefa( s4x 2 s ) |   4 |   1   2  0   1 |  *  *  * 12N   *  * | 0  1  0 0  1  xw&#q
sefa( s 2 o4s ) |   3 |   0   2  1   0 |  *  *  *   * 12N  * | 0  0  1 0  1  q3o
sefa( . x3o4s ) |   6 |   3   0  3   0 |  *  *  *   *   * 4N | 0  0  0 1  1  q3x
----------------+-----+----------------+---------------------+-------------
      s4x3o .   |  12 |  12   0  0  12 |  4  6  4   0   0  0 | N  *  * *  *  x3o3w co variant
      s4x 2 s   |   8 |   4   4  0   4 |  0  2  0   4   0  0 | * 3N  * *  *  xw wx&#q recta
      s 2 o4s   |   4 |   0   4  2   0 |  0  0  0   0   4  0 | *  * 3N *  *  q-tet
      . x3o4s   |  12 |  12   0  6   0 |  4  0  0   0   0  4 | *  *  * N  *  q3x3o tut variant
sefa( s4x3o4s ) |   9 |   3   6  3   3 |  0  0  1   3   3  1 | *  *  * * 4N  wx3oq&#q tricu variant

starting figure: x4x3o4x