Chiroicosafold cuboctaswirlchoron
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Chiroicosafold cuboctaswirlchoron | |
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File:Chiroicosafold cuboctaswirlchoron.png | |
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 480+480+480 phyllic disphenoids, 240 rhombic disphenoids |
Faces | 960+960+960 scalene triangles, 480 isosceles triangles |
Edges | 240+240+480+480+480 |
Vertices | 240 |
Vertex figure | 16-vertex polyhedron with 28 triangular faces |
Measures (edge length 1) | |
Central density | 1 |
Related polytopes | |
Dual | Chirorhombidodecaswirlic diacositetracontachoron |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B3+●I2(20)×2R, order 960 |
Convex | Yes |
Nature | Tame |
The chiroicosafold cuboctaswirlchoron is an isogonal polychoron with 240 rhombic disphenoids, 1440 phyllic disphenoids of three kinds, and 240 vertices. 4 rhombic disphenoids and 24 phyllic disphenoids join at each vertex. It is the third in an infinite family of isogonal chiral cuboctahedral swirlchora.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a chiroicosafold cuboctaswirlchoron of circumradius 1, centered at the origin, are given by, along with their 180° rotations in the xy axis and even sign changes of the first and third coordinates of::
- ±(sin(kπ/10)/√4+2√2, cos(kπ/10)/√4+2√2, cos(kπ/10)/√4-2√2, sin(kπ/10)/√4-2√2),
- ±(sin(kπ/10)/√4-2√2, cos(kπ/10)/√4-2√2, cos(kπ/10)/√4+2√2, sin(kπ/10)/√4+2√2),
- ±(cos((2k-1)π/20)/√4+2√2, -sin((2k-1)π/20)/√4+2√2, cos((2k-1)π/20)/√4-2√2, sin((2k-1)π/20)/√4-2√2),
- ±(cos((2k-1)π/20)/√4-2√2, -sin((2k-1)π/20)/√4-2√2, cos((2k-1)π/20)/√4+2√2, sin((2k-1)π/20)/√4+2√2),
- ±(sin((4k+7)π/40)/√2, cos((4k+7)π/40)/√2, cos((4k-7)π/40)/√2, sin((4k-7)π/40)/√2),
where k is an integer from 0 to 9.