In the geometry of hyperbolic 3-space, the tetrahedral-icosahedral honeycomb is a compact uniform honeycomb, constructed from icosahedron, tetrahedron, and octahedron cells, in an icosidodecahedron vertex figure. It has a single-ring Coxeter diagram , and is named by its two regular cells.
It represents a semiregular honeycomb as defined by all regular cells, although from the Wythoff construction, the octahedron comes from the rectified tetrahedron .
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References
- Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294âÂÂ296)
- Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213)
- Jeffrey R. Weeks The Shape of Space, 2nd edition (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