![]() Full domain ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Half domain ![]() ![]() ![]() ![]() ![]() |
Example compact hyperbolic honeycombs in nonsimplectic domain, a trigonal trapezohedron, with a hexagonal coxeter diagram. the domain is constructed from an index 6 subgroup of [(4,3,4,3)] as [(4,3,4,3*)]:
If two pairs of mirrors have the same ring state, they can be mapped into an extended symmetry with a half domain:
Name | Honeycomb | Cells | Subgroup tiling |
Vertex figure |
Perspective | ||
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Symmetry template | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ↔ ![]() ![]() ![]() ![]() |
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Cubic-octahedral | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ↔ ![]() ![]() ![]() ![]() ↔ ![]() ![]() ![]() ![]() ![]() ![]() |
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Cyclotruncated octahedral-cubic |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ↔ ![]() ![]() ![]() ![]() ↔ ![]() ![]() ![]() ![]() ![]() ![]() |
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Honeycomb | Extended symmetry |
Cells | Subgroup tilings | Vertex figure | |||||
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4.4.4 | 4.6.6 | 3.4.3.4 | 3.3.3.3 | 3.6.6 | 3.3.3 | ||||
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[ ]![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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(2)![]() ![]() ![]() ![]() |
(6)![]() ![]() ![]() ![]() |
(1)![]() ![]() ![]() ![]() |
(2)![]() ![]() ![]() ![]() ![]() ![]() |
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[2]+![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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[3]![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(8)![]() ![]() ![]() ![]() |
(12)![]() ![]() ![]() ![]() |
(6)![]() ![]() ![]() ![]() |
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[6,2+![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(2)![]() ![]() ![]() ![]() |
(6)![]() ![]() ![]() ![]() |
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Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() |
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Vertex figure | 66 | (3.4.3.4)2 | 3.4.6.6.4 | 6.4.6.4 |
Image |
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Dual |
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# | Honeycomb | Cells | Subgroup tiling |
Vertex figure |
Perspective | |||||
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1 | ![]() ![]() ![]() ![]() ![]() |
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2 | ![]() ![]() ![]() ![]() ![]() |
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3 | ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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4 | ![]() ![]() ![]() ![]() ![]() |
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5 | ![]() ![]() ![]() ![]() ![]() |
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6 | ![]() ![]() ![]() ![]() ![]() |
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7 | ![]() ![]() ![]() ![]() ![]() |
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8 | ![]() ![]() ![]() ![]() ![]() |
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9 | ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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10 | ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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11 | ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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12 | ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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