Acronym ..., s∞o2s4x4s
Name edge-snub square prismatic honeycomb
Confer
related CRFs:
10Y4-8T-0  
general polytopal classes:
isogonal  

This honeycomb as a total can not be made uniform: The mere alternated faceting (here starting at grothaph) e.g. would use edges of 3 different sizes: |sefa(s4x)| = x(8,3) = w = 1+sqrt(2) = 2.414214, |s2s| = x(4,2) = q = sqrt(2) = 1.414214 besides the remaining unit edges (refering to elements of s∞o2s4x4s here).

However there is a rescaling according to (x,q,w) → (x,x,u). As such it happens to be a substructure of 10Y4-8T-0, as both the biwedges and the recta then can be dissected accordingly into squippies and tets.


Incidence matrix according to Dynkin symbol

s∞o2x4s4o   (N → ∞)

demi( . . . . . ) | 2N | 1  4 1  2 | 2  8  6 | 4 2 4
------------------+----+-----------+---------+------
demi( . . x . . ) |  2 | N  * *  * | 2  4  0 | 4 0 2  x
      s 2 . s .   |  2 | * 4N *  * | 0  2  2 | 1 1 2  q
      . . . s4o   |  2 | *  * N  * | 0  0  4 | 0 2 2  q
sefa( . . x4s . ) |  2 | *  * * 2N | 1  2  0 | 2 0 1  w
------------------+----+-----------+---------+------
      . . x4s .   |  4 | 2  0 0  2 | N  *  * | 2 0 0  x2w
sefa( s 2 x4s . ) |  4 | 1  2 0  1 | * 4N  * | 1 0 1  xw&#q
sefa( s 2 . s4o ) |  3 | 0  2 1  0 | *  * 4N | 0 1 1  q3o
------------------+----+-----------+---------+------
      s 2 x4s .   |  8 | 4  4 0  4 | 2  4  0 | N * *  xw2wx&#q recta
      s 2 . s4o   |  4 | 0  4 2  0 | 0  0  4 | * N *  q-tet
sefa( s∞o2x4s4o ) |  8 | 2  8 2  2 | 0  4  4 | * * N  xwx2oqo&#qt biwedge

starting figure: x∞o x4x4o

s∞o2s4x4s   (N → ∞)

demi( . . . . . ) | 4N |  1  2  2  1  1  1 | 1 1  4  6  4 | 2  2 2  4
------------------+----+-------------------+--------------+----------
demi( . . . x . ) |  2 | 2N  *  *  *  *  * | 1 1  2  0  2 | 2  0 2  2  x
      s 2 s . .   |  2 |  * 4N  *  *  *  * | 0 0  2  2  0 | 1  1 0  2  q
      s 2 . . s   |  2 |  *  * 4N  *  *  * | 0 0  0  2  2 | 0  1 1  2  q
      . . s 2 s   |  2 |  *  *  * 2N  *  * | 0 0  0  4  0 | 0  2 0  2  q
sefa( . . s4x . ) |  2 |  *  *  *  * 2N  * | 1 0  2  0  0 | 2  0 0  1  w
sefa( . . . x4s ) |  2 |  *  *  *  *  * 2N | 0 1  0  0  2 | 0  0 2  1  w
------------------+----+-------------------+--------------+----------
      . . s4x .   |  4 |  2  0  0  0  2  0 | N *  *  *  * | 2  0 0  0  x2w
      . . . x4s   |  4 |  2  0  0  0  0  2 | * N  *  *  * | 0  0 2  0  x2w
sefa( s 2 s4x . ) |  4 |  1  2  0  0  1  0 | * * 4N  *  * | 1  0 0  1  xw&#q
sefa( s 2 s 2 s ) |  3 |  0  1  1  1  0  0 | * *  * 8N  * | 0  1 0  1  q3o
sefa( s 2 . x4s ) |  4 |  1  0  2  0  0  1 | * *  *  * 4N | 0  0 1  1  xw&#q
------------------+----+-------------------+--------------+----------
      s 2 s4x .   |  8 |  4  4  0  0  4  0 | 2 0  4  0  0 | N  * *  *  xw2wx&#q recta
      s 2 s 2 s   |  4 |  0  2  2  2  0  0 | 0 0  0  4  0 | * 2N *  *  q-tet
      s 2 . x4s   |  8 |  4  0  4  0  0  4 | 0 2  0  0  4 | *  * N  *  xw2wx&#q recta
sefa( s∞o2s4x4s ) |  8 |  2  4  4  2  1  1 | 0 0  2  4  2 | *  * * 2N  xwx2oqo&#qt biwedge

starting figure: x∞o x4x4x

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