Acronym ..., s∞o2s3s6x
Name edge-snub triangular prismatic honeycomb
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This honeycomb as a total can not be made uniform: The mere alternated faceting (here starting at grothaph) e.g. would use edges of 4 different sizes: |sefa(s3s)| = x(6,2) = h = sqrt(3) = 1.732051, |s2s| = x(4,2) = q = sqrt(2) = 1.414214, |sefa(s6x)| = x(12,3) = e = 1+sqrt(3) = 2.732051 besides the remaining unit edges (refering to elements of s∞o2s3s6x here).


Incidence matrix according to Dynkin symbol

s∞o2s3s6x   (N → ∞)

demi( . . . . . ) | 6N |  1  2  2  2  1 |  2  1 1   6  4 |  2 2  4
------------------+----+----------------+----------------+--------
demi( . . . . x ) |  2 | 3N  *  *  *  * |  2  0 1   0  2 |  0 2  3  x
      s 2 s . .   |  2 |  * 6N  *  *  * |  1  0 0   2  0 |  1 0  2  q
      s 2 . s .   |  2 |  *  * 6N  *  * |  0  0 0   2  2 |  1 1  2  q
sefa( . . s3s . ) |  2 |  *  *  * 6N  * |  0  1 0   2  0 |  2 0  1  h
sefa( . . . s6x ) |  2 |  *  *  *  * 3N |  0  0 1   0  2 |  0 2  1  e
------------------+----+----------------+----------------+--------
      s 2 s 2 x   |  4 |  2  2  0  0  0 | 3N  * *   *  * |  0 0  2  x2q
      . . s3s .   |  3 |  0  0  0  3  0 |  * 2N *   *  * |  2 0  0  h3o
      . . . s6x   |  6 |  3  0  0  0  3 |  *  * N   *  * |  0 2  0  e3x
sefa( s 2 s3s . ) |  3 |  0  1  1  1  0 |  *  * * 12N  * |  1 0  1  oh&#q
sefa( s 2 . s6x ) |  4 |  1  0  2  0  1 |  *  * *   * 6N |  0 1  1  xe&#q
------------------+----+----------------+----------------+--------
      s 2 s3s .   |  6 |  0  3  3  6  0 |  0  2 0   6  0 | 2N *  *  ho3oh&#q oct variant
      s 2 . s6x   | 12 |  6  0  6  0  6 |  0  0 2   0  6 |  * N  *  xe3ex&#q ditra
sefa( s∞o2s3s6x ) |  8 |  3  4  4  2  1 |  2  0 0   4  2 |  * * 3N  xxxe&#qr trapezial biwedge

starting figure: x∞o x3x6x

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