| Vertices: | 24 (24[5]) |
| Faces: | 38 (8 equilateral triangles + 24 acute triangles + 6 squares) |
| Edges: | 60 (24 short + 24 medium + 12 long) |
| Symmetry: | Chiral Octahedral (O) |
| Short Edge Angle: | acos(−(sqrt(6*(15*sqrt(3)−22))−9+5*sqrt(3))/6) | ≈139.279979282 degrees |
| Medium Edge Angle: | acos(−(sqrt(6*(15*sqrt(3)−22))+9−5*sqrt(3))/6) | ≈150.593146269 degrees |
| Long Edge Angle: | acos(−(sqrt(1+8*sqrt(3))−5+4*sqrt(3))/6) | ≈164.5293796046 degrees |
| Dual Solid: | Biscribed Pentagonal Icositetrahedron (dextro) |
| (values below based on inscribed radius = 1) |
| Short Edge (24): | sqrt(2*(6+5*sqrt(3)−sqrt(103+60*sqrt(3)))) | ≈0.74220477978959032237 |
| Medium Edge (24): | sqrt(3*(6+5*sqrt(3)−sqrt(103+60*sqrt(3)))) | ≈0.90901149756962447047 |
| Long Edge (12): | sqrt(27+16*sqrt(3)−sqrt(1441+832*sqrt(3))) | ≈1.0138705840028154884 |
| Circumscribed Radius: | sqrt(7+5*sqrt(3)−sqrt(103+60*sqrt(3))) | ≈1.1293511267853134486 |
| Inscribed Radius: | 1 |
| Volume: | 120+74*sqrt(3)−2*sqrt(7411+4280*sqrt(3)) | ≈4.6626021795673548140 |