Steriruncitruncated 5-cube

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Steriruncitruncated 5-cube
Rank5
TypeUniform
Notation
Bowers style acronymCaptint
Coxeter diagramx4x3o3x3x ()
Elements
Tera80 truncated tetrahedral prisms, 80 hexagonal-octagonal duoprisms, 40 truncated cubic prisms, 32 prismatorhombated pentachora, 10 prismatorhombated hexadecachora
Cells320+320 triangular prisms, 320+320 hexagonal prisms, 160 truncated tetrahedra, 240+240 octagonal prisms, 160 cuboctahedra, 80 truncated cubes
Faces640+640 triangles, 480+960+960+960 squares, 640 hexagons, 480 octagons
Edges960+960+1920+1920
Vertices1920
Vertex figureSkewed rectangular pyramidal pyramid, base edge lengths 1 and 2, remaining edge lengths 2 (5), 3 (2), and 2+2 (2)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesPrip–tut–tuttip:
 Tuttip–hip–hodip: 150°
 Ticcup–op–hodip:
 Prip–hip–hodip:
 Proh–tic–ticcup: 135°
 Prip–trip–ticcup:
 Proh–op–hodip:
 Proh–trip–tuttip: 120°
 Proh–co–prip:
Central density1
Number of external pieces242
Level of complexity80
Related polytopes
ArmyCaptint
RegimentCaptint
DualSmall rhombipyramidal pyramidal chilliaenneacosicosateron
ConjugateQuasicelliprismatotruncatopenteractitriacontaditeron
Abstract & topological properties
Flag count307200
Euler characteristic2
OrientableYes
Properties
SymmetryB5, order 3840
ConvexYes
NatureTame

The steriruncitruncated 5-cube, also called the celliprismatotruncated penteractitriacontaditeron, celliprismatotruncatopenteractitriacontaditeron, or captint, is a convex uniform 5-polytope. It consists of 80 truncated tetrahedral prisms, 80 hexagonal-octagonal duoprisms, 40 truncated cubic prisms, 32 prismatorhombated pentachora, and 10 prismatorhombated hexadecachora. 1 prismatorhombated pentachoron, 1 prismatorhombated hexadecachoron, 1 truncated tetrahedral prism, 1 truncated cubic prism, and 2 hexagonal-octagonal duoprisms join at each vertex. As the name suggests, it is the steriruncitruncation of the 5-cube.

Vertex coordinates[edit | edit source]

The vertices of a steriruncitruncated 5-cube of edge length 1 are given by all permutations of:

  • .

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The steriruncitruncated 5-cube is the colonel of a three-member regiment that also includes the small retrocelliprismatotruncatopenteractitriacontaditeron and small lepidocelliprismatotruncatopenteractitriacontaditeron.

External links[edit | edit source]