Template:Tetrahedral vertex figure tessellations
In geometry, there is a sequence of regular honeycombs of the form {6,3,p}, with hexagonal tiling cells:
| {p,3,3} honeycombs | ||||||||
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| Space | S3 | H3 | ||||||
| Form | Finite | Paracompact | Noncompact | |||||
| Name | {3,3,3} | {4,3,3} | {5,3,3} | {6,3,3} | {7,3,3} | {8,3,3} | ... {∞,3,3} | |
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Coxeter diagrams
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| 4 | 
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| 6 |
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| 12 | 
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| 24 |
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| Cells {p,3} 
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 {3,3}
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 {4,3}
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 {5,3}
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 {6,3}
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 {7,3}
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 {8,3}
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 {∞,3}
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References
[edit]- Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
- The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8 (Chapter 10, Regular Honeycombs in Hyperbolic Space) Table III
- N. W. Johnson, R. Kellerhals, J. G. Ratcliffe, S. T. Tschantz, Commensurability classes of hyperbolic Coxeter groups, (2002) H3: p130. [1]