Acronym | ..., s∞o2s4s4s |
Name | full 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 2 different sizes: |sefa(s4s)| = x(8,2) = k = sqrt[2+sqrt(2)] = 1.847759 and |s2s| = x(4,2) = q = sqrt(2) = 1.414214 (refering to elements of s∞o2s4s4s here).
Incidence matrix according to Dynkin symbol
s∞o2s4s4s (N → ∞) demi( . . . . . ) | 4N | 2 2 2 1 2 2 | 1 1 6 6 6 | 2 2 2 5 ------------------+----+-------------------+--------------+---------- s 2 s . . | 2 | 4N * * * * * | 0 0 2 2 0 | 1 1 0 2 q s 2 . s . | 2 | * 4N * * * * | 0 0 2 0 2 | 1 0 1 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( . . s4s . ) | 2 | * * * * 4N * | 1 0 2 0 0 | 2 0 0 1 k sefa( . . . s4s ) | 2 | * * * * * 4N | 0 1 0 0 2 | 0 0 2 1 k ------------------+----+-------------------+--------------+---------- . . s4s . | 4 | 0 0 0 0 4 0 | N * * * * | 2 0 0 0 k4o . . . s4s | 4 | 0 0 0 0 0 4 | * N * * * | 0 0 2 0 k4o sefa( s 2 s4s . ) | 3 | 1 1 0 0 1 0 | * * 8N * * | 1 0 0 1 ok&#q sefa( s 2 s 2 s ) | 3 | 1 0 1 1 0 0 | * * * 8N * | 0 1 0 1 q3o sefa( s 2 . s4s ) | 3 | 0 1 1 0 0 1 | * * * * 8N | 0 0 1 1 ok&#q ------------------+----+-------------------+--------------+---------- s 2 s4s . | 8 | 4 4 0 0 8 0 | 2 0 8 0 0 | N * * * ko4ok&#q squap variant s 2 s 2 s | 4 | 2 0 2 2 0 0 | 0 0 0 4 0 | * 2N * * q-tet s 2 . s4s | 8 | 0 4 4 0 0 8 | 0 2 0 0 8 | * * N * ko4ok&#q squap variant sefa( s∞o2s4s4s ) | 5 | 2 2 2 1 1 1 | 0 0 2 2 2 | * * * 4N tridpy variant starting figure: x∞o x4x4x
s∞o2s4s4o (N → ∞) demi( . . . . . ) | 2N | 2 4 1 4 | 2 12 6 | 4 2 5 ------------------+----+------------+---------+------- s 2 s . . | 2 | 2N * * * | 0 4 0 | 2 0 2 q s 2 . s . | 2 | * 4N * * | 0 2 2 | 1 1 2 q . . . s4o | 2 | * * N * | 0 0 4 | 0 2 2 q sefa( . . s4s . ) | 2 | * * * 4N | 1 2 0 | 2 0 1 k ------------------+----+------------+---------+------- . . s4s . | 4 | 0 0 0 4 | N * * | 2 0 0 k4o sefa( s 2 s4s . ) | 3 | 1 1 0 1 | * 8N * | 1 0 1 ok&#q sefa( s 2 . s4o ) | 3 | 0 2 1 0 | * * 4N | 0 1 1 q3o ------------------+----+------------+---------+------- s 2 s4s . | 8 | 4 4 0 8 | 2 8 0 | N * * ko4ok&#q squap variant s 2 . s4o | 4 | 0 4 2 0 | 0 0 4 | * N * q-tet sefa( s∞o2s4s4o ) | 5 | 2 4 1 2 | 0 4 2 | * * 2N tridpy variant starting figure: x∞o x4x4o
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