| 释义 |
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- References
| Tetrahedral-icosahedral honeycomb | | Type | Compact uniform honeycomb
Semiregular honeycomb | | Schläfli symbol | {(3,3,5,3)} | | Coxeter diagram | label5|branch|3ab|branch_10l}} or {{CDD|label5|branch|3ab|branch_01l}} or {{CDD|node_1|split1|nodes|split2-53|node}} | | Cells | {3,3}
{3,5}
r{3,3} | | Faces | triangular {3}
pentagon {5} | | Vertex figure |
rhombicosidodecahedron | | Coxeter group | [(5,3,3,3)] | | Properties | Vertex-transitive, edge-transitive |
In the geometry of hyperbolic 3-space, the tetrahedral-icosahedral honeycomb is a compact uniform honeycomb, constructed from icosahedron, tetrahedron, and octahedron cells, in a icosidodecahedron vertex figure. It has a single-ring Coxeter diagram, {{CDD|node_1|split1|nodes|split2-53|node}}, and is named by its two regular cells. {{Honeycomb}}It represents a semiregular honeycomb as defined by all regular cells, although from the Wythoff construction, rectified tetrahedral r{3,3}, becomes the regular octahedron {3,4}. Images Wide-angle perspective views
Centered on octahedron | 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
{{DEFAULTSORT:Order-4 Dodecahedral Honeycomb}} 1 : Honeycombs (geometry) |