Runcic 6-cube

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Runcic 6-cube
Rank6
TypeUniform
Notation
Bowers style acronymSirhax
Coxeter diagramx3o3x3o3o *b3o ()
Elements
Peta32 birectified 5-simplices, 32 cantellated 5-simplices, 12 runcic 5-cubes
Tera240 tetrahedral prisms, 192+192 rectified pentachora, 192 small rhombated pentachora, 60 rectified tesseracts
Cells160+480+480 tetrahedra, 960 triangular prisms, 960 octahedra, 480 cuboctahedra
Faces640+1920+1920 triangles, 1440 squares
Edges960+2880
Vertices640
Vertex figureTriangular-triangular pyramidal duoprism, edge lengths 1 (base triangular duoprism and top triangle), 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dipetal anglesDot–rap–sarx:
 Sirhin–srip–sarx:
 Sirhin–rap–dot:
 Sarx–tepe–sarx:
 Sirhin–rit–sirhin: 90°
Central density1
Number of external pieces76
Level of complexity40
Related polytopes
ArmySirhax
RegimentSirhax
ConjugateNone
Abstract & topological properties
Flag count921600
Euler characteristic0
OrientableYes
Properties
SymmetryD6, order 23040
ConvexYes
NatureTame

The runcic 6-cube, also called the cantellated 6-demicube, small rhombidemihexeract, or sirhax, is a convex uniform 6-polytope. It consists of 12 runcic 5-cubes, 32 birectified 5-simplices, and 32 cantellated 5-simplices. 3 runcic 5-cubes, 1 birectified 5-simplex, and 3 cantellated 5-simplices join at each vertex. It can be consrtucted as a birectification of the 6-demicube.

Coordinates[edit | edit source]

The vertex coordinates of a runcic 6-cube, centered at the origin and with unit edge length, are given by all permutations and even sign changes of:

  • .

Representations[edit | edit source]

A runcic 6-cube has the following Coxeter diagrams:

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The runcic 6-cube is the colonel of a regiment that includes 138 uniform members plus 15 fissaries.

External links[edit | edit source]