Runcicantellated 5-orthoplex

From Polytope Wiki
Jump to navigation Jump to search
Runcicantellated 5-orthoplex
File:5-cube t124.svg
Rank5
TypeUniform
Notation
Bowers style acronymPirt
Coxeter diagramo4x3x3o3x (File:CDel node.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.png)
Elements
Tera80 triangular-square duoprisms, 40 truncated octahedral prisms, 32 prismatorhombated pentachora, 10 tesseractihexadecachora
Cells320 triangular prisms, 240 cubes, 320 hexagonal prisms, 160 truncated tetrahedra, 80 cuboctahedra, 80 truncated octahedra
Faces320+320 triangles, 240+480+960 squares, 640 hexagons
Edges960+960+960
Vertices960
Vertex figureSkewed rectangular scalene, base edge lengths 1 and 2, opposite edge length 2, lacing lengths 2 and 3 File:Runcicantellated 5-orthoplex verf.png
Measures (edge length 1)
Circumradius3
Hypervolume
Diteral anglesTope–cube–tisdip:
 Prip–trip–tisdip:
 Tah–toe–tope: 135°
 Prip–hip–tope:
 Prip–co–prip:
 Tah–tut–prip:
Central density1
Number of external pieces162
Level of complexity40
Related polytopes
ArmyPirt
RegimentPirt
DualRhombiscalenic enneacosihexecontateron
ConjugateNone
Abstract & topological properties
Flag count153600
Euler characteristic2
OrientableYes
Properties
SymmetryB5, order 3840
ConvexYes
NatureTame

The runcicantellated 5-orthoplex, also called the prismatorhombated triacontaditeron or pirt, is a convex uniform 5-polytope. It consists of 80 triangular-square duoprisms, 40 truncated octahedral prisms, 10 tesseractihexadecachora, and 32 prismatorhombated pentachora. 2 prismatorhombated pentachora, 1 tesseractihexadecachoron, 1 triangular-square duoprism, and 2 truncated octahedral prisms join at each vertex. As the name suggests, it is the runcicantellation of the 5-orthoplex.

Vertex coordinates[edit | edit source]

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

  • .

Representations[edit | edit source]

A runcicantellated 5-orthoplex has the following Coxeter diagrams:

Gallery[edit | edit source]

Related polytopes[edit | edit source]

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

External links[edit | edit source]