# Steriruncitruncated 5-simplex

The steriruncitruncated 5-simplex, also called the celliprismatotruncated hexateron, celliprismatotruncatododecateron, or captid, is a convex uniform 5-polytope. It consists of 30 truncated tetrahedral prisms, 20 hexagonal duoprisms, and 12 prismatorhombated pentachora. 2 prismatorhombated pentachora, 2 truncated tetrahedral prisms, and 2 hexagonal duoprisms join at each vertex. As the name suggests, it is the steriruncitruncation of the 5-simplex.

Steriruncitruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymCaptid
Coxeter diagramx3x3o3x3x ()
Elements
Tera30 truncated tetrahedral prisms, 20 hexagonal duoprisms, 12 prismatorhombated pentachora
Cells120 triangular prisms, 120+120 hexagonal prisms, 60 truncated tetrahedra, 30 cuboctahedra
Faces240 triangles, 90+180+360 squares, 240 hexagons
Edges360+720
Vertices360
Vertex figureRectangular scalene, base edge lengths 1 and 2, remaining edge lengths 2 (5) and 3 (4)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {5}}\approx 2.23608}$
Hypervolume${\displaystyle {\frac {399{\sqrt {3}}}{5}}\approx 138.21765}$
Diteral anglesTuttip–hip–hiddip: 135°
Prip–tut–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }}$
Prip–hip–hiddip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Prip–trip–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{10}}\right)\approx 108.43495^{\circ }}$
Prip–co–prip: ${\displaystyle \arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }}$
Central density1
Number of external pieces62
Level of complexity40
Related polytopes
ArmyCaptid
RegimentCaptid
DualRhombipyramidal pyramidal triacosihexecontateron
ConjugateNone
Abstract & topological properties
Flag count57600
Euler characteristic2
OrientableYes
Properties
SymmetryA5×2, order 1440
ConvexYes
NatureTame

## Vertex coordinates

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

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

## Representations

A steriruncitruncated 5-simplex has the following Coxeter diagrams:

• x3x3o3x3x (         ) (full symmetry)
• xxxux3xxxoo3ooxxx3xuxxx&#xt (A4 axial, prismatorhombated pentachoron-first)

## Related polytopes

The steriruncitruncated 5-simplex is the colonel of a three-member regiment that also includes the retrocelliprismatotruncatododecateron and lepidocelliprismatotruncatododecateron.