| Vertices: | 13 (1[3] + 6[3] + 3[4] + 3[5]) |
| Faces: | 13 (7 equilateral triangles + 3 squares + 3 regular pentagons) |
| Edges: | 24 (all same length) |
| Symmetry: | 3-fold Pyramidal (C3v) |
| Pentagon-Square Angle (3): | acos(sqrt(10*(5−sqrt(5)))/10) | ≈58.282525589 degrees |
| Pentagon-Triangle Angle (6): | acos(sqrt(15*(5−2*sqrt(5)))/15) | ≈79.187683036 degrees |
| Square-Triangle Angle 1 (6): | acos(−(sqrt(15)−sqrt(3))/6) | ≈110.905157448 degrees |
| Pentagon-Pentagon Angle (3): | acos(−sqrt(5)/5) | ≈116.565051177 degrees |
| Square-Triangle Angle 2 (3): | acos(−(sqrt(3)+sqrt(15))/6) | ≈159.094842552 degrees |
| Triangle-Triangle Angle (3): | acos(−sqrt(5)/3) | ≈221.810314896 degrees |
| (values below based on edge length = 1) |
| Volume: | (12+7*sqrt(5))/12 | ≈2.3043729868748773229 |