Steriruncinated 6-simplex

From Polytope Wiki
(Redirected from Celliprismated heptapeton)
Jump to navigation Jump to search
Steriruncinated 6-simplex
Rank6
TypeUniform
Notation
Bowers style acronymCopal
Coxeter diagramx3o3o3x3x3o ()
Elements
Peta35 triangular-tetrahedral duoprisms, 35 triangular-truncated tetrahedral duoprisms, 21 decachoric prisms, 7 bitruncated hexatera, 7 celliprismated hexatera
Tera105 tetrahedral prisms, 140 triangular duoprisms, 140 triangular-hexagonal duoprisms, 42 truncated pentachora, 21 small prismatodecachora, 105+105 truncated tetrahedral prisms, 42 decachora
Cells105+105 tetrahedra, 210+210+210+420 triangular prisms, 420 hexagonal prisms, 105+210 truncated tetrahedra
Faces140+420+420 triangles, 630+630 squares, 420 hexagons
Edges420+630+630
Vertices420
Vertex figureSkewed Triangular antiprismatic scalene, base edge lengths 1 and 2, opposite edge length 1, lacing lengths 2 and 3
Measures (edge length 1)
Circumradius
Hypervolume
Dipetal anglesTratet–triddip–tratut:
 Decap–tuttip–tratut:
 Bittix–deca–decap:
 Cappix–tepe–tratet:
 Cappix–thiddip–tratut:
 Cappix–tuttip–decap:
 Cappix–tip–bittix:
 Cappix–spid–cappix:
Central density1
Number of external pieces105
Level of complexity120
Related polytopes
ArmyCopal
RegimentCopal
ConjugateNone
Abstract & topological properties
Flag count604800
Euler characteristic0
OrientableYes
Properties
SymmetryA6, order 5040
ConvexYes
NatureTame

The steriruncinated 6-simplex, also called the steriruncinated heptapeton, celliprismated heptapeton, or copal, is a convex uniform 6-polytope. It consists of 7 steritruncated 5-simplices, 7 bitruncated 5-simplices, 21 decachoric prisms, 35 triangular-tetrahedral duoprisms, and 35 triangular-truncated tetrahedral duoprisms. 2 steritruncated 5-simplices, 1 bitruncated 5-simplex, 3 decachoric prisms, 1 triangular-tetrahedral duoprism, and 3 triangular-truncated tetrahedral duoprisms join at each vertex. As the name suggests, it is the steriruncination of the 6-simplex.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a steriruncinated 6-simplex of edge length 1 can be given in 7 dimensions as all permutations of:

  • .

Related polytopes[edit | edit source]

The regiment of the celliprismated heptapeton contains 7 uniform members.

External links[edit | edit source]