Runcitruncated 5-orthoplex

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Runcitruncated 5-orthoplex
Rank5
TypeUniform
Notation
Bowers style acronymPattit
Coxeter diagramo4x3o3x3x ()
Elements
Tera80 square-hexagonal duoprisms, 40 cuboctahedral prisms, 32 prismatorhombated pentachora, 10 rectified icositetrachora
Cells320 triangular prisms, 240+240 cubes, 320 hexagonal prisms, 80 truncated tetrahedra, 80+160 cuboctahedra
Faces320+640 triangles, 480+960+960 squares, 320 hexagons
Edges480+960+1920
Vertices960
Vertex figureWedge pyramid, edge lengths 1 (two edges of base rectangle and top edge of wedge), 2 (sides of wedge, other edges of rectangle base, and lacings to rectangle), and 3 (lacings to top edge)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesCope–cube–shiddip:
 Rico–cube–shiddip:
 Prip–hip–shiddip:
 Rico–co–cope: 135°
 Prip–trip–cope:
 Prip–tut–prip:
 Rico–co–prip:
Central density1
Number of external pieces162
Level of complexity45
Related polytopes
ArmyPattit
RegimentPattit
DualSmall notch-pyramidal enneacosihexecontateron
ConjugateNone
Abstract & topological properties
Flag count172800
Euler characteristic2
OrientableYes
Properties
SymmetryB5, order 3840
ConvexYes
NatureTame

The runcitruncated 5-orthoplex, also called the prismatotruncated triacontaditeron or pattit, is a convex uniform 5-polytope. It consists of 80 square-hexagonal duoprisms, 40 cuboctahedral prisms, 10 rectified icositetrachora, and 32 prismatorhombated pentachora. One rectified icositetrachoron, 1 cuboctahedral prism, 2 prismatorhombated pentachora, and 2 square-hexagonal duoprisms join at each vertex. As the name suggests, it is the runcitruncation of the 5-orthoplex.

Vertex coordinates[edit | edit source]

The vertices of a runcitruncated 5-orthoplex of edge length 1 are given by all permutations of:

  • .

Representations[edit | edit source]

A runcitruncated 5-orthoplex has the following Coxeter diagrams:

  • o4x3o3x3x () (full symmetry)
  • x3o3x3x *b3x () (D5 symmetry)
  • s4x3o3x3x () (D5 symmetry, as alternated faceting)

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The runcitruncated 5-orthoplex is the colonel of a regiment of 11 members. Of these, 7 have full symmetry, while the remaining 4 have D5 symmetry only.

External links[edit | edit source]