| Vertices: | 48 (48[3]) |
| Faces: | 26 (12 squares + 8 regular hexagons + 6 regular octagrams) |
| Edges: | 72 |
| Symmetry: | Full Octahedral (Oh) |
| Hexagon-Square Angle: | acos(sqrt(6)/3) | ≈35.264389683 degrees |
| Octagram-Hexagon Angle: | acos(sqrt(3)/3) | ≈54.735610317 degrees |
| Octagram-Square Angle: | acos(−sqrt(2)/2) | 135 degrees |
| Dual Solid: | Great Disdyakis Dodecahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(13−6*sqrt(2))/2 | ≈1.0623933623853066161 |
| Midscribed Radius: | sqrt(6*(2−sqrt(2)))/2 | ≈0.93737914231134747753 |
| Hexagon Center Radius: | −(sqrt(6)−sqrt(3))/2 | ≈−0.35871946760715040233 |
| Square Center Radius: | (3−sqrt(2))/2 | ≈0.79289321881345247560 |
| Octagram Center Radius: | (2*sqrt(2)−1)/2 | ≈0.91421356237309504880 |
| References: | [1] | Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172. |
| [2] | Johann Pitsch, Über Halbreguläre Sternpolyeder,
Zeitschrift für das Realschulwesen 6 (1881), 9-24, 64-65, 72-89, 216. |
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