Cyclotruncated 7-simplex honeycomb

Cyclotruncated 7-simplex honeycomb
(No image)
Type Uniform honeycomb
Family Cyclotruncated simplectic honeycomb
Schläfli symbol t0,1{3[8]}
Coxeter diagram CDel branch 11.pngCDel 3ab.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel 3ab.pngCDel branch.png
7-face types {36} 7-simplex t0.svg
t0,1{36} 7-simplex t01.svg
t1,2{36} 7-simplex t12.svg
t2,3{36} 7-simplex t23.svg
Vertex figure Elongated 6-simplex antiprism
Symmetry ×22, [[3[8]]]
Properties vertex-transitive

In seven-dimensional Euclidean geometry, the cyclotruncated 7-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 7-simplex, truncated 7-simplex, bitruncated 7-simplex, and tritruncated 7-simplex facets. These facet types occur in proportions of 1:1:1:1 respectively in the whole honeycomb.

StructureEdit

It can be constructed by eight sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 6-simplex honeycomb divisions on each hyperplane.

Related polytopes and honeycombsEdit

This honeycomb is one of 29 unique uniform honeycombs[1] constructed by the   Coxeter group, grouped by their extended symmetry of rings within the regular octagon diagram:

See alsoEdit

Regular and uniform honeycombs in 7-space:

NotesEdit

  1. ^ Weisstein, Eric W. "Necklace". MathWorld., OEIS sequence A000029 30-1 cases, skipping one with zero marks

ReferencesEdit

  • 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]
Fundamental convex regular and uniform honeycombs in dimensions 2-9
          /   /  
{3[3]} δ3 3 3 Hexagonal
{3[4]} δ4 4 4
{3[5]} δ5 5 5 24-cell honeycomb
{3[6]} δ6 6 6
{3[7]} δ7 7 7 222
{3[8]} δ8 8 8 133331
{3[9]} δ9 9 9 152251521
{3[10]} δ10 10 10
{3[n]} δn n n 1k22k1k21