Triacontahexafold octaswirlchoron
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Triacontahexafold octaswirlchoron | |
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File:Triacontahexafold octaswirlchoron.png | |
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 864 phyllic disphenoids, 288 triangular gyroprisms |
Faces | 1728 scalene triangles, 864 isosceles triangles, 288 triangles |
Edges | 216+864+864 |
Vertices | 216 |
Vertex figure | Polyhedron with 8 tetragons and 16 triangles |
Measures (edge length 1) | |
Central density | 1 |
Related polytopes | |
Dual | Cubiswirlic diacosihexadecachoron |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B3●I2(36), order 1728 |
Convex | Yes |
Nature | Tame |
The triacontahexafold octaswirlchoron is an isogonal polychoron with 288 triangular gyroprisms, 864 phyllic disphenoids, and 216 vertices. 8 triangular gyroprisms and 16 phyllic disphenoids join at each vertex. It is the ninth in an infinite family of isogonal octahedral swirlchora.
The ratio between the longest and shortest edges is 1: ≈ 1:4.56783.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a triacontahexafold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations and sign changes of:
- ±(0, 0, sin(kπ/18), cos(kπ/18)),
- ±(sin(kπ/18), cos(kπ/18), 0, 0),
along with 90°, 180° and 270° rotations in the xy axis of:
- ±(sin((k+1/2)π/18)/√2, cos((k+1/2)π/18)/√2, cos((k+1/2)π/18)/√2, sin((k+1/2)π/18)/√2),
where k is an integer from 0 to 17.