Hexagonal tiling-triangular tiling honeycomb
| Hexagonal tiling-triangular tiling honeycomb | |
|---|---|
| Type | Paracompact uniform honeycomb |
| Schläfli symbol | {(3,6,3,6)} or {(6,3,6,3)} |
| Coxeter diagrams |     or  or  or  
|
| Cells | {3,6}  {6,3}  r{6,3} 
|
| Faces | triangular {3} square {4} hexagon {6} |
| Vertex figure |  rhombitrihexagonal tiling |
| Coxeter group | [(6,3)[2]] |
| Properties | Vertex-uniform, edge-uniform |
In the geometry of hyperbolic 3-space, the hexagonal tiling-triangular tiling honeycomb is a paracompact uniform honeycomb, constructed from triangular tiling, hexagonal tiling, and trihexagonal tiling cells, in a rhombitrihexagonal tiling vertex figure.
Symmetry
A lower symmetry form, index 6, of this honeycomb can be constructed with [(6,3,6,3*)] symmetry, represented by a cube fundamental domain, and Coxeter diagram .
See also
References
- Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
- Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
- Jeffrey R. Weeks The Shape of Space, 2nd edition ISBN 0-8247-0709-5 (Chapter 16-17: Geometries on Three-manifolds I,II)
- Norman Johnson Uniform Polytopes, Manuscript
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
- N.W. Johnson: Geometries and Transformations, Manuscript, (2011) Chapter 13: Hyperbolic Coxeter groups