Pentiruncicantitruncated 6-simplex

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Pentiruncicantitruncated 6-simplex
Rank6
TypeUniform
Notation
Bowers style acronymTagopal
Coxeter diagramx3x3x3x3o3x ()
Elements
Peta7 runcicantitruncated 5-simplices
7 stericantitruncated 5-simplices
21 prismatorhombated pentachoric prisms
21 great prismatodecachoric prisms
35 hexagonal-cuboctahedral duoprisms
35 triangular-truncated octahedral duoprisms
Tera210 triangular-square duoprisms
140+140+140 triangular-hexagonal duoprisms
210+210 square-hexagonal duoprisms
105 truncated tetrahedral prisms
105+105 cuboctahedral prisms
105+105 truncated octahedral prisms
42 prismatorhombated pentachora
42 great rhombated pentachora
42 great prismatodecachora
Cells420+420+420+420+420 triangular prisms
420+420+420+420+420 hexagonal prisms
630+630+630 cubes
210 cuboctahedra
210 truncated tetrahedra
210+105 truncated octahedra
Faces840+840 triangles
1260+1260+1260+1260+1260+1260+630 squares
840+420+420 hexagons
Edges2520+2520+1260+1260+1260
Vertices2520
Vertex figureIrregular square tettene
Measures (edge length 1)
Circumradius
Hypervolume
Central density1
Related polytopes
ArmyTagopal
RegimentTagopal
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA6, order 5040
ConvexYes
NatureTame

The pentiruncicantitruncated 6-simplex, also called the pentiruncicantitruncated heptapeton, terigreatoprismated heptapeton, or tagopal, is a convex uniform 6-polytope. It consists of 7 runcicantitruncated 5-simplices, 7 stericantitruncated 5-simplices, 21 prismatorhombated pentachoric prisms, 21 great prismatodecachoric prisms, 35 hexagonal-cuboctahedral duoprisms, and 35 triangular-truncated octahedral duoprisms. 1 runcicantitruncated 5-simplex, 1 stericantitruncated 5-simplex, 1 prismatorhombated pentachoric prism, 2 great prismatodecachoric prisms, 1 hexagonal-cuboctahedral duoprism, and 1 triangular-truncated octahedral duoprism join at each vertex. As the name suggests, it is the pentiruncicantitruncation of the 6-simplex.

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