Omnitruncated 5-cell honeycomb

Omnitruncated 5-cell honeycomb
Omnitruncated 4-simplex honeycomb
(No image)
Type Uniform honeycomb
Family Omnitruncated simplectic honeycomb
Schläfli symbol t0,1,2,3,4{3[5]}
Coxeter–Dynkin diagrams CDel node 1.pngCDel split1.pngCDel nodes 11.pngCDel 3ab.pngCDel branch 11.png
4-face types t0,1,2,3{3,3,3} Schlegel half-solid omnitruncated 5-cell.png
Cell types t0,1,2{3,3} Uniform polyhedron-33-t012.png
{6}x{} Hexagonal prism.png
Face types {4}
{6}
Vertex figure Omnitruncated 4-simplex honeycomb verf.png
Irr. 5-cell
Coxeter groups {\tilde{A}}_4, [3[5]]
Properties vertex-transitive, cell-transitive

In four-dimensional Euclidean geometry, the omnitruncated 4-simplex honeycomb or omnitruncated 5-cell honeycomb is a space-filling tessellation honeycomb. It is composed entirely of omnitruncated 5-cell (omnitruncated 4-simplex) facets.

Coxeter calls this Hinton's honeycomb after C. H. Hinton, who described it in his book The Fourth Dimension in 1906.[1]

Contents

Alernate names

  • Omnitruncated cyclopentachoric tetracomb
  • Great-prismatodecachoric tetracomb

Related polytopes and honeycombs

This honeycomb is one of 7 unique uniform honycombs constructed by the {\tilde{A}}_4 Coxeter group. The Coxeter–Dynkin diagrams of the other six are: CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel branch.png, CDel node 1.pngCDel split1.pngCDel nodes 10lur.pngCDel 3ab.pngCDel branch.png, CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel branch 10l.png, CDel node 1.pngCDel split1.pngCDel nodes 10lur.pngCDel 3ab.pngCDel branch 10l.png, CDel node 1.pngCDel split1.pngCDel nodes 10lur.pngCDel 3ab.pngCDel branch 01l.png,CDel node 1.pngCDel split1.pngCDel nodes 10lur.pngCDel 3ab.pngCDel branch 11.png.

See also

  • Regular and uniform honeycombs in 4-space:

Notes

  1. ^ The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8 (The classification of Zonohededra, page 73)

References

  • Norman Johnson Uniform Polytopes, Manuscript (1991)
  • 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, ISBN 978-0-471-01003-6 [1]
    • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 140
  • Richard Klitzing, 4D, Euclidean tesselations, x3x3x3x3x3*a - otcypit - 140

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