Great hexadecafold tetraantiprismatoswirlchoron
| Great hexadecafold tetraantiprismatoswirlchoron | |
|---|---|
| File:Great hexadecafold tetraantiprismatoswirlchoron.png | |
| Rank | 4 |
| Type | Isogonal |
| Elements | |
| Cells | 256 irregular tetrahedra, 128+128+128 phyllic disphenoids, 32 square gyroprisms |
| Faces | 256+256+256+256+256 scalene triangles, 128 isosceles triangles, 32 squares |
| Edges | 128+128+128+128+128+256 |
| Vertices | 128 |
| Vertex figure | 14-vertex polyhedron with 2 tetragons and 20 triangles |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Great tetraantitegmatoswirlic hecatonicosoctachoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | ((I2(8)×A1)/2)●I2(16), order 256 |
| Convex | Yes |
| Nature | Tame |
The great hexadecafold tetraantiprismatoswirlchoron is an isogonal polychoron with 32 square gyroprisms, 384 phyllic disphenoids of three kinds, and 256 irregular tetrahedras. 2 square gyroprisms, 12 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It is the second in an infinite family of isogonal square antiprismatic swirlchora, the others being the small hexadecafold tetraantiprismatoswirlchoron, small transitional hexadecafold tetraantiprismatoswirlchoron and great transitional hexadecafold tetraantiprismatoswirlchoron.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.96157.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a great hexadecafold pentaantiprismatoswirlchoron, centered at the origin, are given by, along with their 90°, 180°, and 270° rotations in the xy axis of:
- ±(a*sin(kπ/8), a*cos(kπ/8), b*cos(kπ/8), b*sin(kπ/8)),
- ±(b*sin((k+2)π/8), b*cos((k+2)π/8), a*cos(kπ/8), a*sin(kπ/8)),
where a = √2/2, b = (1+√2)/2 and k is an integer from 0 to 7.