Icositetrafold tetraswirlchoron
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| Icositetrafold tetraswirlchoron | |
|---|---|
| File:Icositetrafold tetraswirlchoron.png | |
| Rank | 4 |
| Type | Isogonal |
| Elements | |
| Cells | 288 phyllic disphenoids, 144 rhombic disphenoids, 96 triangular gyroprisms |
| Faces | 576+576 scalene triangles, 96 triangles |
| Edges | 96+144+288+288 |
| Vertices | 96 |
| Vertex figure | 17-vertex polyhedron with 6 tetragons and 18 triangles |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Tetraswirlic enneacontahexachoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | A3●I2(24), order 576 |
| Convex | Yes |
| Nature | Tame |
The icositetrafold tetraswirlchoron is an isogonal polychoron with 96 triangular gyroprisms, 144 rhombic disphenoids, 288 phyllic disphenoids, and 96 vertices. 6 triangular gyroprisms, 6 rhombic disphenoids, and 12 phyllic disphenoids join at each vertex. It is the twelfth in an infinite family of isogonal tetrahedral swirlchora.
The ratio between the longest and shortest edges is 1: ≈ 1:3.83065.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of an icositetrafold tetraswirlchoron of circumradius 1, centered at the origin, are given by:
- ±(0, 0, sin(kπ/12), cos(kπ/12)),
along with 120° and 240° rotations in the xy axis of:
- ±(√6sin(kπ/12)/3, √6cos(kπ/12)/3, √3cos(kπ/12)/3, √3sin(kπ/12)/3),
where k is an integer from 0 to 11.