Runcicantellated 5-simplex

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Runcicantellated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymPirx
Coxeter diagramx3o3x3x3o ()
Elements
Tera20 triangular duoprisms, 15 truncated tetrahedral prisms, 6 decachora, 6 prismatorhombated pentachora
Cells60+60 triangular prisms, 60 hexagonal prisms, 30+30 truncated tetrahedra, 15 cuboctahedra
Faces60+60+60 triangles, 90+180 squares, 120 hexagons
Edges180+180+180
Vertices180
Vertex figureSkewed rectangular scalene, base edge lengths 1 and 2, opposite edge length 1, lacing lengths 2 and 3
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTuttip–trip–triddip: 135°
 Deca–tut–tuttip:
 Prip–trip–triddip:
 Prip–hip–tuttip:
 Prip–tut–deca:
 Prip–co–prip:
Central density1
Number of external pieces47
Level of complexity40
Related polytopes
ArmyPirx
RegimentPirx
DualRhombiscalenic hecatonicoctacontateron
ConjugateNone
Abstract & topological properties
Flag count28800
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
ConvexYes
NatureTame

The runcicantellated 5-simplex, also called the prismatorhombated hexateron or pirx, is a convex uniform 5-polytope. It consists of 20 triangular duoprisms, 15 truncated tetrahedral prisms, 6 decachora, and 6 prismatorhombated pentachora. 2 prismatorhombated pentachora, 1 decachoron, 1 triangular duoprism, and 2 truncated tetrahedral prisms join at each vertex. As the name suggests, it is the runcicantellation of the 5-simplex.

Vertex coordinates[edit | edit source]

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

  • .

Representations[edit | edit source]

A runcicantellated 5-simplex has the following Coxeter diagrams:

  • x3o3x3x3o () (full symmetry)
  • oxxx3xxoo3xxux3ooox&#xt (A4 axial, decachoron-first)

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The runcicantellated 5-simplex is the colonel of a three-member regiment that also includes the retroprismatorhombated hexateron and lepidoprismatorhombated hexateron.

External links[edit | edit source]