# Steritruncated 5-simplex

(Redirected from Celliprismated hexateron)
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${\displaystyle {\frac {2{\sqrt {6}}}{3}}\approx 1.63299}$
Hypervolume${\displaystyle {\frac {1297{\sqrt {3}}}{120}}\approx 18.72058}$
Diteral anglesTuttip–hip–thiddip: 135°
Tepe–trip–thiddip: 135°
Tip–tut–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }}$
Spid–tet–tepe: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }}$
Spid–trip–thiddip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Spid–trip–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{10}}\right)\approx 108.43495^{\circ }}$
Spid–tet–tip: ${\displaystyle \arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }}$
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

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

• ${\displaystyle \left({\frac {3{\sqrt {2}}}{2}},\,{\sqrt {2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,0\right)}$.

## Representations

A steritruncated 5-simplex has the following Coxeter diagrams:

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

## Related polytopes

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