Small transitional triacontafold pentaantiprismatoswirlchoron
| Small transitional triacontafold pentaantiprismatoswirlchoron | |
|---|---|
| File:Small transitional triacontafold pentaantiprismatoswirlchoron.png | |
| Rank | 4 |
| Type | Isogonal |
| Elements | |
| Cells | 300 phyllic disphenoids, 300 triangular gyroprisms, 60 pentagonal gyroprisms |
| Faces | 600 scalene triangles, 600+600 isosceles triangles, 300 triangles, 60 pentagons |
| Edges | 300+300+300+300+600 |
| Vertices | 300 |
| Vertex figure | Polyhedron with 8 tetragons and 4 triangles |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Small transitional pentaantitegmatoswirlic triacosichoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | ((I2(10)×A1)/2)●I2(30), order 600 |
| Convex | Yes |
| Nature | Tame |
The small transitional triacontafold pentaantiprismatoswirlchoron is an isogonal polychoron with 60 pentagonal gyroprisms, 300 triangular gyroprisms, 300 phyllic disphenoids, and 300 vertices. 2 pentagonal gyroprisms, 6 triangular gyroprisms, and 4 phyllic disphenoids join at each vertex. It is the third in an infinite family of isogonal pentagonal antiprismatic swirlchora, the others being the small triacontafold pentaantiprismatoswirlchoron, great triacontafold pentaantiprismatoswirlchoron and great transitional triacontafold pentaantiprismatoswirlchoron.
The ratio between the longest and shortest edges is 1: ≈ 1:2.95630.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a small transitional triacontafold pentaantiprismatoswirlchoron, centered at the origin, are given by, along with their 72°, 144°, 216° and 288° rotations in the xy axis of:
- ±(2sin(kπ/15)/√10+2√5, 2cos(kπ/15)/√10+2√5, 2cos(kπ/15)/√10-2√5, 2sin(kπ/15)/√10-2√5),
- ±(2sin(kπ/15)/√10-2√5, 2cos(kπ/15)/√10-2√5, -2cos(kπ/15)/√10+2√5, -2sin(kπ/15)/√10+2√5),
where k is an integer from 0 to 14.