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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