Acronym snich
Name s4s3s4s (?),
(full) snub cubical honeycomb
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Even so 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(s4s)| = x(8) = sqrt[2+sqrt(2)] = 1.847759, |s2s| = x(4) = sqrt(2) = 1.414214, and |sefa(s3s)| = x(6) = sqrt(3) = 1.732051 (refering to elements of s4s3s4s here).


Incidence matrix according to Dynkin symbol

s4s3s4s   (N → ∞)

demi( . . . . ) | 24N |   1   1   1   2   2   2 |  1  1  1   3   3   3   3 | 1  1  1 1   4
----------------+-----+-------------------------+--------------------------+--------------
      s 2 s .   |   2 | 12N   *   *   *   *   * |  0  0  0   2   0   2   0 | 1  0  1 0   2
      s . 2 s   |   2 |   * 12N   *   *   *   * |  0  0  0   0   2   2   0 | 0  1  1 0   2
      . s 2 s   |   2 |   *   * 12N   *   *   * |  0  0  0   0   2   0   2 | 0  1  0 1   2
sefa( s4s . . ) |   2 |   *   *   * 24N   *   * |  1  0  0   1   1   0   0 | 1  1  0 0   1
sefa( . s3s . ) |   2 |   *   *   *   * 24N   * |  0  1  0   1   0   0   1 | 1  0  0 1   1
sefa( . . s4s ) |   2 |   *   *   *   *   * 24N |  0  0  1   0   0   1   1 | 0  0  1 1   1
----------------+-----+-------------------------+--------------------------+--------------
      s4s . .   |   4 |   0   0   0   4   0   0 | 6N  *  *   *   *   *   * | 1  1  0 0   0
      . s3s .   |   3 |   0   0   0   0   3   0 |  * 8N  *   *   *   *   * | 1  0  0 1   0
      . . s4s   |   4 |   0   0   0   0   0   4 |  *  * 6N   *   *   *   * | 0  0  1 1   0
sefa( s4s3s . ) |   3 |   1   0   0   1   1   0 |  *  *  * 24N   *   *   * | 1  0  0 0   1
sefa( s4s 2 s ) |   3 |   0   1   1   1   0   0 |  *  *  *   * 24N   *   * | 0  1  0 0   1
sefa( s 2 s4s ) |   3 |   1   1   0   0   0   1 |  *  *  *   *   * 24N   * | 0  0  1 0   1
sefa( . s3s4s ) |   3 |   0   0   1   0   1   1 |  *  *  *   *   *   * 24N | 0  0  0 1   1
----------------+-----+-------------------------+--------------------------+--------------
      s4s3s .     24 |  12   0   0  24  24   0 |  6  8  0  24   0   0   0 | N  *  * *   *
      s4s 2 s      8 |   0   4   4   8   0   0 |  2  0  0   0   8   0   0 | * 3N  * *   *
      s 2 s4s      8 |   4   4   0   0   0   8 |  0  0  2   0   0   8   0 | *  * 3N *   *
      . s3s4s     24 |   0   0  12   0  24  24 |  0  8  6   0   0   0  24 | *  *  * N   *
sefa( s4s3s4s )    4 |   1   1   1   1   1   1 |  0  0  0   1   1   1   1 | *  *  * * 24N
or
demi( . . . . )   | 12N |   2  1   4   2 |  2  1   6   6 | 2  2   4
------------------+-----+----------------+---------------+---------
      s 2 s .   & |   2 | 12N  *   *   * |  0  0   2   2 | 1  1   2
      s . 2 s     |   2 |   * 6N   *   * |  0  0   0   4 | 0  2   2
sefa( s4s . . ) & |   2 |   *  * 24N   * |  1  0   1   1 | 1  1   1
sefa( . s3s . )   |   2 |   *  *   * 12N |  0  1   2   0 | 2  0   1
------------------+-----+----------------+---------------+---------
      s4s . .   & |   4 |   0  0   4   0 | 6N  *   *   * | 1  1   0
      . s3s .     |   3 |   0  0   0   3 |  * 4N   *   * | 2  0   0
sefa( s4s3s . ) & |   3 |   1  0   1   1 |  *  * 24N   * | 1  0   1
sefa( s4s 2 s )   |   3 |   1  1   1   0 |  *  *   * 24N | 0  1   1
------------------+-----+----------------+---------------+---------
      s4s3s .   &   24 |  12  0  24  24 |  6  8  24   0 | N  *   *
      s4s 2 s   &    8 |   4  4   8   0 |  2  0   0   8 | * 3N   *
sefa( s4s3s4s )      4 |   2  1   2   1 |  0  0   2   2 | *  * 12N

starting figure: x4x3x4x

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