Acronym | cytatoh (old: batatoh) |
Name |
cyclotruncated tetrahedral-octahedral honeycomb (but not the hyperbolic cyclotruncated octahedral-tetrahedral honeycomb cytoth), bitruncated tetrahedral-octahedral honeycomb, bitruncated alternated-cubic honeycomb, quarter cubic honeycomb |
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Vertex figure |
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This honeycomb also can be described as s4o3o4s', i.e. as sequential applications of alternated facetings, according to x4o3o4x → s4o3o4x (= x3o3o *b4x) → x3o3o *b4s' (cf. below).
By virtue of an outer symmetry this is a non-quasiregular monotoxal honeycomb, that is all edges belong to the same equivalence class.
Incidence matrix according to Dynkin symbol
x3x3o3o3*a (N → ∞) . . . . | 4N ♦ 3 3 | 6 3 3 | 3 3 1 1 -----------+----+-------+----------+-------- x . . . | 2 | 6N * | 2 2 0 | 1 2 1 0 . x . . | 2 | * 6N | 2 0 2 | 2 1 0 1 -----------+----+-------+----------+-------- x3x . . | 6 | 3 3 | 4N * * | 1 1 0 0 x . . o3*a | 3 | 3 0 | * 4N * | 0 1 1 0 . x3o . | 3 | 0 3 | * * 4N | 1 0 0 1 -----------+----+-------+----------+-------- x3x3o . ♦ 12 | 6 12 | 4 0 4 | N * * * x3x . o3*a ♦ 12 | 12 6 | 4 4 0 | * N * * x . o3o3*a ♦ 4 | 6 0 | 0 4 0 | * * N * . x3o3o ♦ 4 | 0 6 | 0 0 4 | * * * N
or . . . . | 2N ♦ 6 | 6 6 | 6 2 --------------+----+----+-------+---- x . . . & | 2 | 6N | 2 2 | 3 1 --------------+----+----+-------+---- x3x . . | 6 | 6 | 2N * | 2 0 x . . o3*a & | 3 | 3 | * 4N | 1 1 --------------+----+----+-------+---- x3x3o . & ♦ 12 | 18 | 4 4 | N * x . o3o3*a & ♦ 4 | 6 | 0 4 | * N
x3x3o3/2o3/2*a (N → ∞) . . . . | 4N ♦ 3 3 | 6 3 3 | 3 3 1 1 ---------------+----+-------+----------+-------- x . . . | 2 | 6N * | 2 2 0 | 1 2 1 0 . x . . | 2 | * 6N | 2 0 2 | 2 1 0 1 ---------------+----+-------+----------+-------- x3x . . | 6 | 3 3 | 4N * * | 1 1 0 0 x . . o3/2*a | 3 | 3 0 | * 4N * | 0 1 1 0 . x3o . | 3 | 0 3 | * * 4N | 1 0 0 1 ---------------+----+-------+----------+-------- x3x3o . ♦ 12 | 6 12 | 4 0 4 | N * * * x3x . o3/2*a ♦ 12 | 12 6 | 4 4 0 | * N * * x . o3/2o3/2*a ♦ 4 | 6 0 | 0 4 0 | * * N * . x3o3/2o ♦ 4 | 0 6 | 0 0 4 | * * * N
x3o3o *b4s (N → ∞) demi( . . . . ) | 4N ♦ 3 3 | 3 6 3 | 1 3 1 3 -------------------+----+-------+----------+-------- demi( x . . . ) | 2 | 6N * | 2 2 0 | 1 2 0 1 . o . *b4s | 2 | * 6N | 0 2 2 | 0 1 1 2 -------------------+----+-------+----------+-------- demi( x3o . . ) | 3 | 3 0 | 4N * * | 1 1 0 0 sefa( x3o . *b4s ) | 6 | 3 3 | * 4N * | 0 1 0 1 sefa( . o3o *b4s ) | 3 | 0 3 | * * 4N | 0 0 1 1 -------------------+----+-------+----------+-------- demi( x3o3o . ) ♦ 4 | 6 0 | 4 0 0 | N * * * x3o . *b4s ♦ 12 | 12 6 | 4 4 0 | * N * * . o3o *b4s ♦ 4 | 0 6 | 0 0 4 | * * N * sefa( x3o3o *b4s ) ♦ 12 | 6 12 | 0 4 4 | * * * N starting figure: x3o3o *b4x
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