Acronym	casch
Name	cantic 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 edge-alternated faceting (here starting at grich) e.g. would use edges of 4 different sizes: |s4o| = q = sqrt(2) = 1.414214, |sefa(x4s)| = w = 1+sqrt(2) = 2.414214, |s3s| = h = sqrt(3) = 1.732051, as well as the here surviving x = 1 (refering to elements of x4s3s4o here).

Incidence matrix according to Dynkin symbol

x4s3s4o   (N → ∞)

demi( . . . . ) | 12N |  1  1  1   4 |  1  2  1   4   3 | 2 1  3
----------------+-----+--------------+------------------+-------
demi( x . . . ) |   2 | 6N  *  *   * |  1  0  1   2   0 | 2 0  2  x
      . . s4o   |   2 |  * 6N  *   * |  0  0  1   0   2 | 0 1  2  q
sefa( x4s . . ) |   2 |  *  * 6N   * |  1  0  0   2   0 | 2 0  1  w
sefa( . s3s . ) |   2 |  *  *  * 24N |  0  1  0   1   1 | 1 1  1  h
----------------+-----+--------------+------------------+-------
      x4s . .   |   4 |  2  0  2   0 | 3N  *  *   *   * | 2 0  0  x w
      . s3s .   |   3 |  0  0  0   3 |  * 8N  *   *   * | 1 1  0  h3o
      x . s4o   |   4 |  2  2  0   0 |  *  * 3N   *   * | 0 0  2  x q
sefa( x4s3s . ) |   4 |  1  0  1   2 |  *  *  * 12N   * | 1 0  1  xw&#h
sefa( . s3s4o ) |   3 |  0  1  0   2 |  *  *  *   * 12N | 0 1  1  oq&#h
----------------+-----+--------------+------------------+-------
      x4s3s .   |  24 | 12  0 12  24 |  6  8  0  12   0 | N *  *  xwX wXx Xxw&#zh (X = x+2q = q+w) pyritohedral sirco variant
      . s3s4o   |  12 |  0  6  0  24 |  0  8  0   0  12 | * N  *  Qqo qoQ oQq&#zh (Q = 2q) pyritohedral ike variant
sefa( x4s3s4o ) |   6 |  2  2  1   4 |  0  0  1   2   2 | * * 6N  wx oq&#h 2-cup variant (wedge)

starting figure: x4x3x4o

s3s3s *b4x

demi( . . .    . ) | 24N |   1   1   2   2   1 |  1  1  1  1   3   2   2 |  1 1 1   3
-------------------+-----+---------------------+-------------------------+-----------
demi( . . .    x ) |   2 | 12N   *   *   *   * |  0  1  0  1   0   1   1 |  0 1 1   2  x
      s 2 s    .   |   2 |   * 12N   *   *   * |  0  1  0  0   2   0   0 |  1 0 0   2  q
sefa( s3s .    . ) |   2 |   *   * 24N   *   * |  1  0  0  0   1   1   0 |  1 1 0   1  h
sefa( . s3s    . ) |   2 |   *   *   * 24N   * |  0  0  1  0   1   0   1 |  1 0 1   1  h
sefa( . s . *b4x ) |   2 |   *   *   *   * 12N |  0  0  0  1   0   1   1 |  0 1 1   1  w
-------------------+-----+---------------------+-------------------------+-----------
      s3s .    .   |   3 |   0   0   3   0   0 | 8N  *  *  *   *   *   * |  1 1 0   0  h3o
      s 2 s    x   |   4 |   2   2   0   0   0 |  * 6N  *  *   *   *   * |  0 0 0   2  x q
      . s3s    .   |   3 |   0   0   0   3   0 |  *  * 8N  *   *   *   * |  1 0 1   0  h3o
      . s . *b4x   |   4 |   2   0   0   0   2 |  *  *  * 6N   *   *   * |  0 1 1   0  x w
sefa( s3s3s    . ) |   3 |   0   1   1   1   0 |  *  *  *  * 24N   *   * |  1 0 0   1  oq&#h
sefa( s3s . *b4x ) |   4 |   1   0   2   0   1 |  *  *  *  *   * 12N   * |  0 1 0   1  xw&#h
sefa( . s3s *b4x ) |   4 |   1   0   0   2   1 |  *  *  *  *   *   * 12N |  0 0 1   1  xw&#h
-------------------+-----+---------------------+-------------------------+-----------
      s3s3s    .   |  12 |   0   6  12  12   0 |  4  0  4  0  12   0   0 | 2N * *   *  Qqo qoQ oQq&#zh (Q = 2q) pyritohedral ike variant
      s3s . *b4x   |  24 |  12   0  24   0  12 |  8  0  0  6   0  12   0 |  * N *   *  xwX wXx Xxw&#zh (X = x+2q = q+w) pyritohedral sirco variant
      . s3s *b4x   |  24 |  12   0   0  24  12 |  0  0  8  6   0   0  12 |  * * N   *  xwX wXx Xxw&#zh (X = x+2q = q+w) pyritohedral sirco variant
sefa( s3s3s *b4x ) |   6 |   2   2   2   2   1 |  0  1  0  0   2   1   1 |  * * * 12N  wx oq&#h 2-cup variant (wedge)

starting figure: x3x3x *b4x