| Vertices: | 144 (24[3] + 24[3] + 24[3] + 24[3] + 24[3] + 24[3]) |
| Faces: | 74 (12 squares + 8 regular hexagons + 48 irregular hexagons + 6 regular octagons) |
| Edges: | 216 (24 short + 168 medium + 24 long) |
| Symmetry: | Full Octahedral (Oh) |
| (values below based on medium edge length = 1) |
| Short Edge (24): | (−2+3*sqrt(2)+2*sqrt(3)
−sqrt(3*(22−13*sqrt(2)+12*sqrt(3)−8*sqrt(6))))/3 | ≈0.63682057096651000602 |
| Medium Edge (168): | 1 |
| Long Edge (24): | (−2+4*sqrt(2)+2*sqrt(3)−sqrt(6)
−sqrt(6*(10−5*sqrt(2)+4*sqrt(3)−4*sqrt(6))))/3 | ≈1.3585327044181696899 |
| Max Vertex Radius: | sqrt(6*(28+7*sqrt(2)+4*sqrt(3)+6*sqrt(6)
+4*sqrt(3*(8+2*sqrt(2)+2*sqrt(3)+3*sqrt(6)))))/6 | ≈3.9105532237440182029 |
| Volume: | 2*(792−63*sqrt(2)+54*sqrt(3)+198*sqrt(6)
+2*sqrt(3*(117340+9847*sqrt(2)
+9240*sqrt(3)+47049*sqrt(6))))/27 | ≈226.39349069791957008 |