| Vertices: | 48 (24[4] + 24[4]) |
| Faces: | 50 (8 equilateral triangles + 6 squares + 12 rhombi
+ 24 isosceles trapezoids) |
| Edges: | 96 (24 short + 48 medium + 24 long) |
| Symmetry: | Full Octahedral (Oh) |
| (values below based on edge-scribed radius = 1) |
| Short Edge (24): | sqrt(root[8th-order polynomial]) | ≈0.46972045047354051787 |
| Medium Edge (48): | sqrt(root[8th-order polynomial]) | ≈0.52334558639128002957 |
| Long Edge (24): | sqrt(root[8th-order polynomial]) | ≈0.57697072230901954127 |
| Rhombus Length: | sqrt(root[8th-order polynomial]) | ≈0.77711656911613231437 |
| Rhombus Width: | sqrt(root[8th-order polynomial]) | ≈0.70117918479237712119 |
| Rhombus Angle: | acos(root[8th-order polynomial]) | ≈84.118807718 degrees |
| Edge-scribed Radius: | 1 |
| Volume: | root[8th-order polynomial] | ≈4.0465896055629099430 |