Steriruncitruncated 5-simplex

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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
Hypervolume
Diteral anglesTuttip–hip–hiddip: 135°
 Prip–tut–tuttip:
 Prip–hip–hiddip:
 Prip–trip–tuttip:
 Prip–co–prip:
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

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.

Vertex coordinates[edit | edit source]

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

  • .

Representations[edit | edit source]

A steriruncitruncated 5-simplex has the following Coxeter diagrams:

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

Gallery[edit | edit source]

Related polytopes[edit | edit source]

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

External links[edit | edit source]