| Vertices: | 10 (10[4]) |
| Faces: | 12 (10 equilateral triangles + 2 regular pentagons) |
| Edges: | 20 |
| Symmetry: | 5-fold Antiprismatic (D5v) |
| Pentagon-Triangle Angle: | acos(−sqrt(15*(5−2*sqrt(5)))/15) | ≈100.812316964 degrees |
| Triangle-Triangle Angle: | acos(−sqrt(5)/3) | ≈138.189685104 degrees |
| Dual Solid: | Pentagonal Trapezohedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(2*(5+sqrt(5)))/4 | ≈0.95105651629515357212 |
| Midscribed Radius: | (1+sqrt(5))/4 | ≈0.80901699437494742410 |
| Pentagon Center Radius: | sqrt(10*(5+sqrt(5)))/20 | ≈0.42532540417601996609 |
| Triangle Center Radius: | (3*sqrt(3)+sqrt(15))/12 | ≈0.75576131407617073048 |
| Volume: | (5+2*sqrt(5))/6 | ≈1.5786893258332632321 |
| 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). |
|