Runcinated 6-cube
Runcinated 6-cube | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Spox |
Coxeter diagram | x4o3o3x3o3o () |
Elements | |
Peta | 240 square-tetrahedral duoprisms 192 rectified pentachoric prisms 64 birectified 5-simplices 12 runcinated 5-cubes |
Tera | 960 tetrahedral prisms 384+384 rectified pentachora 960 triangular-square duoprisms 960 octahedral prisms 60 small disprismatotesseractihexadecachora |
Cells | 960+960 tetrahedra 1920+3840 triangular prisms 1920 octahedra 160+1440 cubes |
Faces | 3840+3840 triangles, 960+5760 squares |
Edges | 1920+5760 |
Vertices | 1280 |
Vertex figure | Triangle atop gyrated triangular duoprism, edge lengths 1 (base triangular duoprism), √2 (top triangle and side edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dipetal angles | Dot–rap–rappip: |
Rappip–tepe–squatet: | |
Span–tisdip–squatet: 120° | |
Span–ope–rappip: | |
Span–rap–dot: | |
Span–sidpith–span: 90° | |
Central density | 1 |
Number of external pieces | 508 |
Level of complexity | 56 |
Related polytopes | |
Army | Spox |
Regiment | Spox |
Conjugate | Quasiprismated hexeract |
Abstract & topological properties | |
Flag count | 2580480 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B6, order 46080 |
Convex | Yes |
Nature | Tame |
The runcinated 6-cube, also called the runcinated dodecapeton, small prismated hexeract, or spox, is a convex uniform 6-polytope. It consists of 12 runcinated 5-cubes, 64 birectified 5-simplices, 192 rectified pentachoric prisms, and 240 square-tetrahedral duoprisms. 3 runcinated 5-cubes, 1 birectified 5-simplex, 3 rectified pentachoric prisms, and 3 square-tetrahedral duoprisms join at each vertex. As the name suggests, it is the runcination of the 6-cube.
The runcinated 6-cube contains the vertices and edges of the small rhombated 5-cubic prism, square-truncated tesseractic duoprism, octagonal-small rhombated tesseractic duoprism, truncated cubic-small rhombicuboctahedral duoprism, octagonal-truncated cubic duoprismatic prism, and the octagonal trioprism.
Vertex coordinates[edit | edit source]
The coordinates of a runcinated 6-cube, centered at the origin and with unit edge length, are given by all permutations of:
- .
Gallery[edit | edit source]
-
B5 orthographic projection
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B4
-
B3
-
B2
-
A5
-
A3
Related polytopes[edit | edit source]
The runcinated 6-cube is the colonel of a regiment that includes 138 uniform members plus 15 fissaries.
External links[edit | edit source]
- Klitzing, Richard. "spox".
- Wikipedia contributors. "Runcinated 6-cube".