Runcinated 6-orthoplex
Runcinated 6-orthoplex | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Spog |
Coxeter diagram | o4o3x3o3o3x () |
Elements | |
Peta | 160 triangular-octahedral duoprisms 60 icositetrachoric prisms 64 runcinated 5-simplices 12 birectified 5-cubes |
Tera | 1280 triangular duoprisms 384 rectified pentachora 480+960 octahedral prisms 192 small prismatodecachora 120 icositetrachora |
Cells | 240+960 tetrahedra 1920+1920+3840 triangular prisms 480+1920 octahedra |
Faces | 960+3840+3840 triangles, 5760 squares |
Edges | 1440+5760 |
Vertices | 960 |
Vertex figure | Triangle atop gyrated triangular-square duoprism, edge lengths 1 (base duoprism and top triangle), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dipetal angles | Icope–ope–troct: |
Spix–triddip–troct: 135° | |
Nit–ico–icope: 135° | |
Spix–ope–icope: | |
Spix–spid–spix | |
Nit–rap–spix: | |
Central density | 1 |
Number of external pieces | 296 |
Level of complexity | 56 |
Related polytopes | |
Army | Spog |
Regiment | Spog |
Conjugate | None |
Abstract & topological properties | |
Flag count | 2580480 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B6, order 46080 |
Convex | Yes |
Nature | Tame |
The runcinated 6-orthoplex, also called the runcinated hexacontatetrapeton, small prismated hexacontatetrapeton, or spog, is a convex uniform 6-polytope. It consists of 12 birectified 5-cubes, 64 runcinated 5-simplices, 60 icositetrachoric prisms, and 160 triangular-octahedral duoprisms. 1 birectified 5-cube, 4 runcinated 5-simplices, 3 icositetrachoric prisms, and 3 triangular-octahedral duoprisms join at each vertex. As the name suggests, it is the runcination of the 6-orthoplex.
The runcinated 6-orthoplex contains the vertices and edges of the square-rectified icositetrachoric duoprism and cuboctahedral-truncated octahedral duoprism.
Vertex coordinates[edit | edit source]
The coordinates of a runcinated 6-orthoplex, centered at the origin and with unit edge length, are given by all permutations of:
- .
Representations[edit | edit source]
A runcinated 6-orthoplex has the following Coxeter diagrams:
- o4o3x3o3o3x () (full symmetry)
- o3x3o3o3x *b3o () (D6 symmetry)
Gallery[edit | edit source]
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B5 orthographic projection
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B4
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B3
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B2
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A5
-
A3
External links[edit | edit source]
- Klitzing, Richard. "spog".
- Wikipedia contributors. "Runcinated 6-orthoplex".