Runcitruncated 5-simplex

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Runcitruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymPattix
Coxeter diagramx3x3o3x3o ()
Elements
Tera15 octahedral prisms, 20 triangular-hexagonal duoprisms, 6 small rhombated pentachora, 6 prismatorhombated pentachora
Cells60+60+60 triangular prisms, 30 octahedra, 60 hexagonal prisms, 15 truncated tetrahedra, 30 cuboctahedra
Faces60+120+120 triangles, 180+180 squares, 60 hexagons
Edges90+180+360
Vertices180
Vertex figureWedge pyramid, edge lengths 1 (base square and top edge of wedge), 2 (sides of wedge and lacings to square), and 3 (lacings to top edge)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesOpe–trip–thiddip: 135°
 Srip–oct–ope:
 Srip–trip–thiddip:
 Prip–hip–thiddip:
 Prip–trip–ope:
 Prip–co–srip:
 Prip–tut–prip:
Central density1
Number of external pieces47
Level of complexity45
Related polytopes
ArmyPattix
RegimentPattix
DualNotch-pyramidal hecatonoctacontateron
ConjugateNone
Abstract & topological properties
Flag count32400
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
ConvexYes
NatureTame

The runcitruncated 5-simplex, also called the prismatotruncated hexateron or pattix, is a convex uniform 5-polytope. It consists of 15 octahedral prisms, 20 triangular-hexagonal duoprisms, 6 small rhombated pentachora, and 6 prismatorhombated pentachora. One small rhombated pentachoron, 1 octahedral prism, 2 prismatorhombated pentachora, and 2 triangular-hexagonal duoprisms join at each vertex. As the name suggests, it is the runcitruncation of the 5-simplex.

Vertex coordinates[edit | edit source]

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

  • .

Representations[edit | edit source]

A runcitruncated 5-simplex has the following Coxeter diagrams:

  • x3x3o3x3o () (full symmetry)
  • xuxx3ooxx3xxxo3ooox&#xt (A4 axial, small rhombated pentachoron-first)

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The runcitruncated 5-simplex is the colonel of a regiment of 7 members.

External links[edit | edit source]