Runcitruncated 5-orthoplex
Runcitruncated 5-orthoplex | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Pattit |
Coxeter diagram | o4x3o3x3x () |
Elements | |
Tera | 80 square-hexagonal duoprisms, 40 cuboctahedral prisms, 32 prismatorhombated pentachora, 10 rectified icositetrachora |
Cells | 320 triangular prisms, 240+240 cubes, 320 hexagonal prisms, 80 truncated tetrahedra, 80+160 cuboctahedra |
Faces | 320+640 triangles, 480+960+960 squares, 320 hexagons |
Edges | 480+960+1920 |
Vertices | 960 |
Vertex figure | Wedge 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 angles | Cope–cube–shiddip: |
Rico–cube–shiddip: | |
Prip–hip–shiddip: | |
Rico–co–cope: 135° | |
Prip–trip–cope: | |
Prip–tut–prip: | |
Rico–co–prip: | |
Central density | 1 |
Number of external pieces | 162 |
Level of complexity | 45 |
Related polytopes | |
Army | Pattit |
Regiment | Pattit |
Dual | Small notch-pyramidal enneacosihexecontateron |
Conjugate | None |
Abstract & topological properties | |
Flag count | 172800 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B5, order 3840 |
Convex | Yes |
Nature | Tame |
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]
-
B4 or D5 orthographic projection
-
B3, D4, or A2
-
B2
-
A3
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]
- Klitzing, Richard. "pattit".
- Wikipedia contributors. "Runcitruncated 5-orthoplex".