Acronym esch Name edge-snub cubic 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 edge-alternated faceting (here starting at giddich) e.g. would use edges of 5 different sizes: |s4s| = k = sqrt[2+sqrt(2)] = 1.847759, |s2s| = q = sqrt(2) = 1.414214, |s3s| = h = sqrt(3) = 1.732051, |sefa(x4s)| = w = 1+sqrt(2) = 2.414214, as well as the here surviving x = 1 (refering to elements of s4s3s4x here).

Incidence matrix according to Dynkin symbol

```s4s3s4x   (N → ∞)

demi( . . . . ) | 24N |   1   1   2   2   1 |  1  1  1   3   2   2   2 | 1  1  1 1   3
----------------+-----+---------------------+--------------------------+--------------
demi( . . . x ) |   2 | 12N   *   *   *   * |  0  0  1   0   2   1   1 | 0  1  1 1   2  x
s 2 s .   |   2 |   * 12N   *   *   * |  0  0  0   2   0   2   0 | 1  0  1 0   2  q
sefa( s4s . . ) |   2 |   *   * 24N   *   * |  1  0  0   1   1   0   0 | 1  1  0 0   1  k
sefa( . s3s . ) |   2 |   *   *   * 24N   * |  0  1  0   1   0   0   1 | 1  0  0 1   1  h
sefa( . . s4x ) |   2 |   *   *   *   * 12N |  0  0  1   0   0   1   1 | 0  0  1 1   1  w
----------------+-----+---------------------+--------------------------+--------------
s4s . .   |   4 |   0   0   4   0   0 | 6N  *  *   *   *   *   * | 1  1  0 0   0  k4o
. s3s .   |   3 |   0   0   0   3   0 |  * 8N  *   *   *   *   * | 1  0  0 1   0  h3o
. . s4x   |   4 |   2   0   0   0   2 |  *  * 6N   *   *   *   * | 0  0  1 1   0  x w
sefa( s4s3s . ) |   3 |   0   1   1   1   0 |  *  *  * 24N   *   *   * | 1  0  0 0   1  (q,h,k)-{3}
sefa( s4s 2 x ) |   4 |   2   0   2   0   0 |  *  *  *   * 12N   *   * | 0  1  0 0   1  x k
sefa( s 2 s4x ) |   4 |   1   2   0   0   1 |  *  *  *   *   * 12N   * | 0  0  1 0   1  xw&#q
sefa( . s3s4x ) |   4 |   1   0   0   2   1 |  *  *  *   *   *   * 12N | 0  0  0 1   1  xw&#h
----------------+-----+---------------------+--------------------------+--------------
s4s3s .   |  24 |   0  12  24  24   0 |  6  8  0  24   0   0   0 | N  *  * *   *  snic variant
s4s 2 x   |   8 |   4   0   8   0   0 |  2  0  0   0   4   0   0 | * 3N  * *   *  (k,x)-4p
s 2 s4x   |   8 |   4   4   0   0   4 |  0  0  2   0   0   4   0 | *  * 3N *   *  xw wx&#q recta
. s3s4x   |  24 |  12   0   0  24  12 |  0  8  6   0   0   0  12 | *  *  * N   *  pyritohedral sirco variant
sefa( s4s3s4x ) |   6 |   2   2   2   2   1 |  0  0  0   2   1   1   1 | *  *  * * 12N  wx2ox&#(q,h) slanted wedge (trip variant)
```