Icosidifold tetraswirlchoron
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Icosidifold tetraswirlchoron | |
---|---|
File:Icosidifold tetraswirlchoron.png | |
Rank | 4 |
Type | Isogonal |
Elements | |
Cells | 264+264+264 phyllic disphenoids |
Faces | 528+528 scalene triangles, 264+264 isosceles triangles |
Edges | 88+264+264+264 |
Vertices | 88 |
Vertex figure | 20-vertex polyhedron with 30 triangular faces |
Measures (edge length 1) | |
Central density | 1 |
Related polytopes | |
Dual | Tetraswirlic octacontoctachoron |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | A3●I2(22), order 528 |
Convex | Yes |
Nature | Tame |
The icosidifold tetraswirlchoron is an isogonal polychoron with 792 phyllic disphenoids of three kinds and 88 vertices. 36 disphenoids join at each vertex. It is the eleventh in an infinite family of isogonal tetrahedral swirlchora.
The ratio between the longest and shortest edges is 1: ≈ 1:3.73032.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of an icosidifold tetraswirlchoron of circumradius 1, centered at the origin, are given by:
- ±(0, 0, sin(kπ/11), cos(kπ/11)),
along with 120° and 240° rotations in the xy axis of:
- ±(√6sin(kπ/11)/3, √6cos(kπ/11)/3, √3cos(kπ/11)/3, √3sin(kπ/11)/3),
where k is an integer from 0 to 10.