Dodecafold pyritocubiswirlchoron
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| Dodecafold pyritocubiswirlchoron | |
|---|---|
| File:Dodecafold pyritocubiswirlchoron.png | |
| Rank | 4 |
| Type | Isogonal |
| Elements | |
| Cells | 288 phyllic disphenoids, 144+144 rhombic disphenoids |
| Faces | 576+576 scalene triangles |
| Edges | 96+144+144+288 |
| Vertices | 96 |
| Vertex figure | 14-vertex polyhedron with 24 triangular faces |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Pyritooctaswirlic enneacontahexachoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | (B3/2)●I2(12)×2R, order 576 |
| Convex | Yes |
| Nature | Tame |
The dodecafold pyritocubiswirlchoron is an isogonal polychoron with 288 rhombic disphenoids of two kinds, 288 phyllic disphenoids, and 96 vertices. 12 rhombic and 12 phyllic disphenoids join at each vertex. It is the second in an infinite family of isogonal pyritohedral cubic swirlchora and is one of several isogonal polychora that can be formed as hulls of various combinations of 4 icositetrachora.
The ratio between the longest and shortest edges is 1: ≈ 1:1.77615.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a dodecafold pyritocubiswirlchoron of circumradius 1, centered at the origin, are:
- ±(0, 0, sin(kπ/6), cos(kπ/6)),
- ±(sin(kπ/6), cos(kπ/6), 0, 0),
along with 120° and 240° rotations in the xy axis of:
- ±(√6sin(kπ/6)/3, √6cos(kπ/6)/3, √3cos(kπ/6)/3, √3sin(kπ/6)/3),
- ±(√3cos(kπ/6)/3, √3sin(kπ/6)/3, -√6sin(kπ/6)/3, -√6cos(kπ/6)/3),
where k is an integer from 0 to 5.