Pentiruncitruncated 6-simplex

pentiruncitruncated 6-simplex
A6 Coxeter plane projection (7-gonal symmetry)
Type	uniform polypeton
Schläfli symbol	t0,1,3,5{3,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces	126
4-faces	1491
Cells	5565
Faces	8610
Edges	5670
Vertices	1260
Vertex figure
Coxeter groups	A6, [3,3,3,3,3]
Properties	convex

In six-dimensional geometry, a pentiruncitruncated 6-simplex is a uniform 6-polytope.

Alternate names

• Tericellirhombated heptapeton (Acronym: tocral) (Jonathan Bowers)

The vertices of the pentiruncitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,1,1,2,3,4). This construction is based on facets of the pentiruncitruncated 7-orthoplex.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Dihedral symmetry	[7]	[6]	[5]
Ak Coxeter plane	A3	A2
Graph
Dihedral symmetry	[4]	[3]

Related uniform 6-polytopes

This is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A₆ Coxeter plane orthographic projections.

See also

Other 6-polytopes:

• 6-simplex - {3,3,3,3,3}
• 6-orthoplex (hexacross) - {3,3,3,3,4}
• 6-cube (hexeract) - {4,3,3,3,3}
• 6-demicube (demihexeract) - {3^1,3,1}

External links

• Olshevsky, George. "Cross polytope". Glossary for Hyperspace. Archived from the original on 4 February 2007.
• Polytopes of Various Dimensions
• Multi-dimensional Glossary
• Richard Klitzing 6D quasiregulars, (multi)prisms, non-prismatic Wythoffian polyterons x3x3o3x3o3x