| Vertices: | 24 (24[5]) |
| Faces: | 38 (32 equilateral triangles + 6 squares) |
| Edges: | 60 |
| Symmetry: | Chiral Octahedral (O) |
| Square-Triangle Angle: | acos(−sqrt(11−2*cbrt(17+3*sqrt(33))
−2*cbrt(17−3*sqrt(33)))/3) | ≈142.983430074 degrees |
| Triangle-Triangle Angle: | acos(−sqrt(3*(11+4*cbrt(17+3*sqrt(33))
+4*cbrt(17−3*sqrt(33))))/9) | ≈153.234587713 degrees |
| Dual Solid: | Pentagonal Icositetrahedron |
| (values below based on midscribed radius = 1) |
| Edge Length: | 2*sqrt(3*(5−cbrt(19+3*sqrt(33))
−cbrt(19−3*sqrt(33))))/3 | ≈0.801781129201327280647 |
| Circumscribed Radius: | sqrt(3*(8−cbrt(19+3*sqrt(33))
−cbrt(19−3*sqrt(33))))/3 | ≈1.0773640261238718692 |
| Midscribed Radius: | 1 |
| Square Center Radius: | sqrt(3*(cbrt(19+3*sqrt(33))
+cbrt(19−3*sqrt(33))−2))/3 | ≈0.91612594942734873530 |
| Triangle Center Radius: | sqrt(4+cbrt(19+3*sqrt(33))
+cbrt(19−3*sqrt(33)))/3 | ≈0.97284578346453266494 |
| Volume: | 8*sqrt(3*(cbrt(1124803+344589*sqrt(33))
−cbrt(344589*sqrt(33)−1124803)−44))/9 | ≈4.0664527252304884030 |