Acronym | ..., s∞o2s4x4s |
Name | edge-snub square prismatic honeycomb |
Confer | |
External links |
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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