Acronym	edge-snub square prismatic honeycomb
Name	edge-snub square 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(s4x)| = x(8,3) = w = 1+sqrt(2) = 2.414214, |sefa(s4s)| = x(8,2) = k = sqrt[2+sqrt(2)] = 1.847759, |s2s| = x(4,2) = q = sqrt(2) = 1.414214 besides the remaining unit edges (refering to elements of s∞o2s4s4x here).

Incidence matrix according to Dynkin symbol

s∞o2s4s4x   (N → ∞)

demi( . . . . . ) | 4N |  1  2  2  2  1 |  2 1 1  6  4 | 2 2  4
------------------+----+----------------+--------------+-------
demi( . . . . x ) |  2 | 2N  *  *  *  * |  2 0 1  0  2 | 0 2  3  x
      s 2 s . .   |  2 |  * 4N  *  *  * |  1 0 0  2  0 | 1 0  2  q
      s 2 . s .   |  2 |  *  * 4N  *  * |  0 0 0  2  2 | 1 1  2  q
sefa( . . s4s . ) |  2 |  *  *  * 4N  * |  0 1 0  2  0 | 2 0  1  k
sefa( . . . s4x ) |  2 |  *  *  *  * 2N |  0 0 1  0  2 | 0 2  1  w
------------------+----+----------------+--------------+-------
      s 2 s 2 x   |  4 |  2  2  0  0  0 | 2N * *  *  * | 0 0  2  x2q
      . . s4s .   |  4 |  0  0  0  4  0 |  * N *  *  * | 2 0  0  k4o
      . . . s4x   |  4 |  2  0  0  0  2 |  * * N  *  * | 0 2  0  x2w
sefa( s 2 s4s . ) |  3 |  0  1  1  1  0 |  * * * 8N  * | 1 0  1  ok&#q
sefa( s 2 . s4x ) |  4 |  1  0  2  0  1 |  * * *  * 4N | 0 1  1  xw&#q
------------------+----+----------------+--------------+-------
      s 2 s4s .   |  8 |  0  4  4  8  0 |  0 2 0  8  0 | N *  *  ko4ok&#q squap variant
      s 2 . s4x   |  8 |  4  0  4  0  4 |  0 0 2  0  4 | * N  *  xw2wx&#q recta
sefa( s∞o2s4s4x ) |  8 |  3  4  4  2  1 |  2 0 0  4  2 | * * 2N  trapezium biwedge

starting figure: x∞o x4x4x