Runcicantitruncated 6-simplex

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Runcicantitruncated 6-simplex
Rank6
TypeUniform
Notation
Bowers style acronymGapil
Coxeter diagramx3x3x3x3o3o ()
Elements
Peta7 runcicantitruncated 5-simplices
7 cantitruncated 5-simplices
21 truncated pentachoric prisms
35 hexagonal-tetrahedral duoprisms
Tera140 triangular-hexagonal duoprisms
105+105 tetrahedral prisms
105 truncated tetrahedral prism
42 great rhombated pentachora
42 truncated pentachora
21 great prismatodecachora
Cells420+420 triangular prisms
210+210 hexagonal prisms
210 tetrahedra
210 truncated tetrahedra
105+35 truncated octahedra
Faces840 triangles
630+630+210 squares
420+140+140 hexagons
Edges1260+420+420+420
Vertices840
Vertex figureIrregular triangular tettene
Measures (edge length 1)
Circumradius
Hypervolume
Central density1
Related polytopes
ArmyGapil
RegimentGapil
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA6, order 5040
ConvexYes
NatureTame

The runcicantitruncated 6-simplex, also called the runcicantitruncated heptapeton, great prismated heptapeton, or gapil, is a convex uniform 6-polytope. It consists of 7 runcicantitruncated 5-simplices, 7 cantitruncated 5-simplices, 21 truncated pentachoric prisms, and 35 hexagonal-tetrahedral duoprisms. 3 runcicantitruncated 5-simplices, 1 cantitruncated 5-simplex, 1 truncated pentachoric prism, and 1 hexagonal-tetrahedral duoprism join at each vertex. As the name suggests, it is the runcicantitruncation of the 6-simplex.

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