Stericated 5-cube

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Stericated 5-cube
Rank5
TypeUniform
Notation
Bowers style acronymScant
Coxeter diagramx4o3o3o3x ()
Elements
Tera32 pentachora, 80 tetrahedral prisms, 80 triangular-square duoprisms, 10+40 tesseracts
Cells160 tetrahedra, 320 triangular prisms, 80+240 cubes
Faces320 triangles, 240+480 squares
Edges320+320
Vertices160
Vertex figureTetrahedral antipodium, edge lengths 1 (base 1) and 2 (base 2 and sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesPen–tet–tepe:
 Tepe–trip–tisdip: 150°
 Tes–cube–tisdip:
 Tes–cube–tes: 135°
Central density1
Number of external pieces242
Level of complexity16
Related polytopes
ArmyScant
RegimentScant
DualTetrahedral-antitegmatic hecatonhexecontateron
ConjugateQuasicellipenteractitriacontaditeron
Abstract & topological properties
Flag count61440
Euler characteristic2
OrientableYes
Properties
SymmetryB5, order 3840
ConvexYes
NatureTame

The stericated 5-cube, also called the small cellated penteract, small cellipenteractitriacontaditeron, or scant, is a convex uniform 5-polytope. It consists of 32 regular pentachora, 80 tetrahedral prisms, 80 triangular-square duoprisms, and 10+40 tesseracts. 1 pentachoron, 4 tetrahedral prisms, 6 triangular-square duoprisms, and 1+4 tesseracts join at each vertex. It can be formed by expanding the facets of either the 5-cube or its dual 5-orthoplex outward.

The stericated 5-cube contains the vertices of a small disprismatotesseractihexadecachoric prism, square-small rhombicuboctahedral duoprism, and octagonal-cubic duoprism.

Vertex coordinates[edit | edit source]

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

  • .

Representations[edit | edit source]

A stericated 5-cube has the following Coxeter diagrams:

  • x4o3o3o3x () (full symmetry)
  • xxxx4oooo3oooo3oxxo&#xt (B4 axial, tesseract-first)
  • wx xx4oo3oo3ox&#zx (B4×A1 symmetry)
  • xx4ox xx4oo3xo&#zx (B3×B2 symmetry)

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The stericated 5-cube is the colonel of a regiment that contains a total of 15 uniform members. This regiment also has many subsymmetric scaliform members.

External links[edit | edit source]