| 释义 |
- Cyclotruncated tetrahedral-square tiling honeycomb
- See also
- References
| Tetrahedral-square tiling honeycomb | | Type | Paracompact uniform honeycomb | | Schläfli symbol | {(4,4,3,3)} or {(3,3,4,4)} | | Coxeter diagrams | node|split1-44|nodes_10luru|split2|node}} | | Cells | {3,3}
{4,4}
r{4,3} | | Faces | triangle {3}
square {4} | | Vertex figure |
Rhombicuboctahedron | | Coxeter group | [(4,4,3,3)] | | Properties | Vertex-transitive, edge-transitive |
In the geometry of hyperbolic 3-space, the tetrahedral-square tiling honeycomb is a paracompact uniform honeycomb, constructed from tetrahedron, cuboctahedron and square tiling cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, {{CDD|node|split1-44|nodes_10luru|split2|node}}, and is named by its two regular cells. {{Honeycomb}}{{-}} Cyclotruncated tetrahedral-square tiling honeycomb | Cyclotruncated tetrahedral-square tiling honeycomb | | Type | Paracompact uniform honeycomb | | Schläfli symbol | t0,1{(4,4,3,3)} | | Coxeter diagrams | node_1|split1-44|nodes_10luru|split2|node}} | | Cells | {4,3}
t{4,3}
{3,3}
t{4,3} | | Faces | triangle {3}
square {4}
octagon {8} | | Vertex figure |
Triangular antiprism | | Coxeter group | [(4,4,3,3)] | | Properties | Vertex-transitive |
The cyclotruncated tetrahedral-square tiling honeycomb is a paracompact uniform honeycomb, constructed from tetrahedron, cube, truncated cube and truncated square tiling cells, in a triangular antiprism vertex figure. It has a Coxeter diagram, {{CDD|node_1|split1-44|nodes_10luru|split2|node}}. See also - Convex uniform honeycombs in hyperbolic space
- List of regular polytopes
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, (2018) Chapter 13: Hyperbolic Coxeter groups
1 : Honeycombs (geometry) |