| 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 (laevo) |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(3*(10+cbrt(199+3*sqrt(33))
+cbrt(199−3*sqrt(33))))/6 | ≈1.3437133737446017013 |
| Midscribed Radius: | sqrt(3*(7+cbrt(199+3*sqrt(33))
+cbrt(199−3*sqrt(33))))/6 | ≈1.2472231679936432518 |
| Square Center Radius: | sqrt(3*(4+cbrt(199+3*sqrt(33))
+cbrt(199−3*sqrt(33))))/6 | ≈1.14261350892596209348 |
| Triangle Center Radius: | sqrt(3*(6+cbrt(199+3*sqrt(33))
+cbrt(199−3*sqrt(33))))/6 | ≈1.2133558000218923103 |
| Volume: | sqrt(188+cbrt(3*(2149479+15037*sqrt(33)))
+cbrt(3*(2149479−15037*sqrt(33))))/3 | ≈7.889477399975390206451 |