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| Tetrahedron-cube honeycomb | | Type | Compact uniform honeycomb | | Schläfli symbol | {(4,3,3,3)} or {(3,3,3,4)} | | Coxeter diagram | label4|branch_10r|3ab|branch}} or {{CDD|label4|branch_01r|3ab|branch}} or {{CDD|node_1|split1-43|nodes|split2|node}} | | Cells | {3,3}
{4,3}
r{4,3} | | Faces | triangular {3}
square {4} | | Vertex figure |
rhombicuboctahedron | | Coxeter group | [(4,3,3,3)] | | Properties | Vertex-transitive, edge-transitive |
In the geometry of hyperbolic 3-space, the tetrahedron-cube honeycomb is a compact uniform honeycomb, constructed from cube, tetrahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, {{CDD|node_1|split1-43|nodes|split2|node}}, and is named by its two regular cells. {{Honeycomb}} Images Wide-angle perspective view
Centered on cube | See also - Convex uniform honeycombs in hyperbolic space
- List of regular polytopes
- Hyperbolic tetrahedral-octahedral honeycomb
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
{{DEFAULTSORT:Order-4 Dodecahedral Honeycomb}} 1 : Honeycombs (geometry) |