| Vertices: | 8 (8[4]) |
| Faces: | 10 (8 equilateral triangles + 2 squares) |
| Edges: | 16 |
| Symmetry: | 4-fold Antiprismatic (D4v) |
| Square-Triangle Angle: | acos(−(sqrt(6)−sqrt(3))/3) | ≈103.836160479 degrees |
| Triangle-Triangle Angle: | acos(−(2*sqrt(2)−1)/3) | ≈127.551602906 degrees |
| Dual Solid: | Tetragonal Trapezohedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(2*(4+sqrt(2)))/4 | ≈0.82266438800803628873 |
| Midscribed Radius: | sqrt(2*(2+sqrt(2)))/4 | ≈0.65328148243818826393 |
| Square Center Radius: | sqrt(2*sqrt(2))/4 | ≈0.42044820762685727152 |
| Triangle Center Radius: | sqrt(6*(4+3*sqrt(2)))/12 | ≈0.58604040983818133611 |
| Volume: | sqrt(4+3*sqrt(2))/3 | ≈0.95699998183671671759 |
| References: | [1] | Johannes Kepler, Harmonices Mundi (1619). |
| [2] | Johannes Kepler with E. J. Aiton, A. M. Duncan,
and J. V. Field, translators, The Harmony of the World,
American Philosophical Society (1997). |
|