Steritruncated 5-simplex

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Steritruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymCappix
Coxeter diagramx3x3o3o3x ()
Elements
Tera15 tetrahedral prisms, 20 triangular-hexagonal duoprisms, 6 truncated pentachora, 15 truncated tetrahedral prisms, 6 small prismatodecachora
Cells30+30 tetrahedra, 60+60+60 triangular prisms, 60 hexagonal prisms, 30 truncated tetrahedra
Faces120+120 triangles, 90+180 squares, 60 hexagons
Edges60+180+180
Vertices120
Vertex figureSkew triangular antiprismatic pyramid, edge lengths 1 (base triangles), 2 (sides of antiprism and lacings to one base), and 3 (lacings to other base)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTuttip–hip–thiddip: 135°
 Tepe–trip–thiddip: 135°
 Tip–tut–tuttip:
 Spid–tet–tepe:
 Spid–trip–thiddip:
 Spid–trip–tuttip:
 Spid–tet–tip:
Central density1
Number of external pieces62
Level of complexity40
Related polytopes
ArmyCappix
RegimentCappix
DualTriangular-antitegmatic pyramidal hecatonicosateron
ConjugateNone
Abstract & topological properties
Flag count28800
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
ConvexYes
NatureTame

The steritruncated 5-simplex, also called the celliprismated hexateron or cappix, is a convex uniform 5-polytope. It consists of 15 tetrahedral prisms, 20 triangular-hexagonal duoprisms, 15 truncated tetrahedral prisms, 6 truncated pentachora, and 6 small prismatodecachora. One small prismatodecachoron, 1 tetrahedral prism, 1 truncated pentachoron, 3 truncated tetrahedral prisms, and 3 triangular-hexagonal duoprisms join at each vertex. As the name suggests, it is the steritruncation of the 5-simplex.

Vertex coordinates[edit | edit source]

The vertices of a steritruncated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:

  • .

Representations[edit | edit source]

A steritruncated 5-simplex has the following Coxeter diagrams:

  • x3x3o3o3x () (full symmetry)
  • xuxx3ooxx3oooo3xxxo&#xt (A4 axial, small prismatodecachoron-first)

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The steritruncated 5-simplex is the colonel of a regiment of 7 members.

External links[edit | edit source]