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1 52 honeycomb

152 honeycomb
(No image)
Type
Family
Schläfli symbol
Coxeter symbol
Coxeter-Dynkin diagram
8-face types
7-face types
6-face types
5-face types
4-face type
Cells
Faces
Vertex figure
Coxeter group

In geometry, the 152 honeycomb is a uniform tessellation of 8-dimensional Euclidean space. It contains 142 and 151 facets, in a birectified 8-simplex vertex figure. It is the final figure in the 1k2 polytope family.

Construction

It is created by a Wythoff construction upon a set of 9 hyperplane mirrors in 8-dimensional space.

The facet information can be extracted from its Coxeter-Dynkin diagram. :

Removing the node on the end of the 2-length branch leaves the 8-demicube, 151. :

Removing the node on the end of the 5-length branch leaves the 142. :

The vertex figure is determined by removing the ringed node and ringing the neighboring node. This makes the birectified 8-simplex, 052. :

References

  • Coxeter The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, (Chapter 3: Wythoff's Construction for Uniform Polytopes)
  • Coxeter Regular Polytopes (1963), Macmillan Company
    • Regular Polytopes, Third edition, (1973), Dover edition, (Chapter 5: The Kaleidoscope)
  • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, wiley.com, , GoogleBook
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45]
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9-polytopes e8-(mathematics) honeycombs-(geometry)
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