Runcicantellated 5-orthoplex
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:
- o4x3x3o3x (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) (full symmetry)
- x3x3o3x *b3x (File:CDel nodea 1.pngFile:CDel 3a.pngFile:CDel branch 11.pngFile:CDel 3a.pngFile:CDel nodea.pngFile:CDel 3a.pngFile:CDel nodea 1.png) (D5 symmetry)
- s4x3x3o3x (File:CDel node h.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) (D5 symmetry, as alternated faceting)
Gallery[edit | edit source]
-
B4 or D5 orthographic projection
-
B3, D4, or A2
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B2
-
A3
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]
- Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#835).
- Klitzing, Richard. "pirt".
- Wikipedia contributors. "Runcicantellated 5-orthoplex".