| Vertices: | 38 (32[3] + 6[4]) |
| Faces: | 24 (irregular pentagons) |
| Edges: | 60 (12 short + 24 medium + 24 long) |
| Symmetry: | Chiral Octahedral (O) |
| Short Edge Angle: | acos(−(99−74*sqrt(3)
+sqrt(3*(6487+3764*sqrt(3))))/282) | ≈126.657193242 degrees |
| Medium Edge Angle: | acos(−(35*sqrt(3)−50
+sqrt(3*(241+400*sqrt(3))))/94) | ≈132.537319853 degrees |
| Long Edge Angle: | acos(−(35*sqrt(3)
−3+sqrt(3*(241+400*sqrt(3))))/141) | ≈141.632610391 degrees |
| Dual Solid: | Biscribed Snub Cube (laevo) |
| (values below based on circumscribed radius = 1) |
| Short Edge (12): | sqrt(3*(11−4*sqrt(3)−sqrt(1+8*sqrt(3))))/3 | ≈0.26919376455618979793 |
| Medium Edge (24): | sqrt(3*(5*sqrt(3)−3
−sqrt(6*(15*sqrt(3)−22))))/3 | ≈0.50763159299964177698 |
| Long Edge (24): | sqrt(3*(15−5*sqrt(3)
−sqrt(6*(15*sqrt(3)−22))))/3 | ≈0.69583557132062191899 |
| Circumscribed Radius: | 1 |
| Inscribed Radius: | 1/sqrt(7+5*sqrt(3)−sqrt(103+60*sqrt(3))) | ≈0.88546420708543487113 |
| Volume: | 2*(15*sqrt(3)−22+sqrt(52*sqrt(3)−89))/3 | ≈3.3423638184311954732 |