Digonal double tetraswirlprism
The digonal double tetraswirlprism is a convex isogonal polychoron that consists of 16 tetragonal disphenoids, 48 rhombic disphenoids of three kinds, 32 phyllic disphenoids, and 64 irregular tetrahedra. 2 tetragonal disphenoids, 6 rhombic disphenoids, 4 phyllic disphenoids, and 8 irregular tetrahedra join at each vertex. It can be obtained as the convex hull of two orthogonal digonal-digonal tetraswirlprisms. However, it cannot be made uniform. Together with its dual, it is the third in an infinite family of digonal antiprismatic swirlchora. It is the third in an infinite family of isogonal digonal prismatic swirlchora, the other being the square duoantiprism.
| Digonal double tetraswirlprism | |
|---|---|
| Rank | 4 |
| Type | Isogonal |
| Elements | |
| Cells | 64 irregular tetrahedra, 32 phyllic disphenoids, 16+16+16 rhombic disphenoids, 16 tetragonal disphenoids |
| Faces | 64+64+64+64 scalene triangles, 64 isosceles triangles |
| Edges | 16+16+32+32+32+32+32 |
| Vertices | 32 |
| Vertex figure | 12-vertex polyhedron with 20 triangular faces |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Dual | Digonal double tetraswirltegum |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | (I2(8)≀S2)+/4, order 64 |
| Convex | Yes |
| Nature | Tame |
This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1: ≈ 1:1.84776) would yield a square duoantiprism instead.
