Runcinated 2 21 polytope
(Redirected from Small prismated icosiheptaheptacontadipeton)
Runcinated 2 21 polytope | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Spojak |
Coxeter diagram | x3o3o3x3o *c3x () |
Elements | |
Peta | 720 triangular duoprismatic prisms, 216 small rhombated pentachoric prisms, 72 runcinated 5-simplices, 27 runcic 5-cubes, 27 runcinated 5-orthoplexes |
Tera | 1440 triangular duoprisms, 432 rectified pentachora, 2160+2160 triangular-square duoprisms, 1080 octahedral prisms, 216+432 small prismatodecachora, 1080 cuboctahedral prisms, 432 small rhombated pentachora, 270 rectified tesseracts |
Cells | 1080+2160 tetrahedra, 3×2160+3×4320 triangular prisms, 1080+2160 octahedra, 6480 cubes, 2160 cuboctahedra |
Faces | 3×4320+8640 triangles, 6480+6480+12960 squares |
Edges | 6480+6480+12960 |
Vertices | 4320 |
Vertex figure | Triangle atop triangular fastegium, edge lengths 1 (triangle prism cell and opposing triangles) and √2 (all other edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dipetal angles | Srippip–tisdip–tratrip: |
Spix–triddip–tratrip: 150° | |
Sirhin–srip–srippip: | |
Spix–ope–srippip: | |
Spat–tisdip–tratrip: 135° | |
Spat–cope–srippip: | |
Spat–spid–spix: | |
Sirhin–rap–spix: | |
Central density | 1 |
Number of external pieces | 1062 |
Level of complexity | 168 |
Related polytopes | |
Army | Spojak |
Regiment | Spojak |
Conjugate | None |
Abstract & topological properties | |
Flag count | 8709120 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | E6, order 51840 |
Convex | Yes |
Nature | Tame |
The runcinated 221 polytope, also called the small prismated icosiheptaheptacontadipeton or spojak, is a convex uniform 6-polytope. It consists of 27 runcinated 5-orthoplexes, 27 runcic 5-cubes, 72 runcinated 5-simplices, 216 small rhombated pentachoric prisms, and 720 triangular duoprismatic prisms. 2 runcinated 5-orthoplexes, 1 runcic 5-cube, 1 runcinated 5-simplex, 3 small rhombated pentachoric prisms, and 3 triangular duoprismatic prisms join at each vertex. As the name suggests, it is the runcination of the 221 polytope.
External links[edit | edit source]
- Klitzing, Richard. "spojak".