| Vertices: | 38 (32[3] + 6[4]) |
| Faces: | 24 (mirror-symmetric pentagons) |
| Edges: | 60 (36 short + 24 long) |
| Symmetry: | Chiral Octahedral (O) |
| Dihedral Angle: | acos((1−cbrt(2*(283+21*sqrt(33)))
−cbrt(2*(283−21*sqrt(33))))/21) | ≈136.309232892 degrees |
| Dual Solid: | Snub Cube |
| (values below based on edge-scribed radius = 1) |
| Short Edge (36): | sqrt(2*(2−cbrt(2*(13+3*sqrt(33)))
+cbrt(2*(3*sqrt(33)−13)))) | ≈0.47582932325308764446 |
| Long Edge (24): | sqrt(3*(4−cbrt(17+3*sqrt(33))
+cbrt(3*sqrt(33)−17)))/3 | ≈0.67550794762750470428 |
| [3]-Vertex Radius (32): | sqrt(2*(4−cbrt(2*(13+3*sqrt(33)))
+cbrt(2*(3*sqrt(33)−13))))/2 | ≈1.0279121490754318561 |
| [4]-Vertex Radius (6): | sqrt(6*(cbrt(6*(9+sqrt(33)))
+cbrt(6*(9−sqrt(33)))))/6 | ≈1.0915529689177336240 |
| Edge-scribed Radius: | 1 |
| Inscribed Radius: | sqrt(42*(20+cbrt(2*(283+21*sqrt(33)))
+cbrt(2*(283−21*sqrt(33)))))/42 | ≈0.92819137798557160941 |
| Volume: | 4*sqrt(6*(27−4*cbrt(3*(63+11*sqrt(33)))
+4*cbrt(3*(11*sqrt(33)−63))))/3 | ≈3.8385914460594167728 |