Stellated octahedron
| Type | Regular compound |
|---|---|
| Coxeter symbol | {4,3}[2{3,3}]{3,4} |
| Schläfli symbols | {{3,3}} a{4,3} ß{2,4} ßr{2,2} |
| Coxeter diagrams | ∪ |
| Stellation core | regular octahedron |
| Convex hull | cube |
| Index | UC4, W19 |
| Polyhedra | two tetrahedra |
| Faces | 8 triangles |
| Edges | 12 |
| Vertices | 8 |
| Dual polyhedron | self-dual |
| Symmetry group | octahedral symmetry, pyritohedral symmetry |
The stellated octahedron is the only stellation of the octahedron. It is also called the stella octangula (Latin for "eight-pointed star"), a name given to it by Johannes Kepler in 1609, though it was known to earlier geometers. It was depicted in Pacioli's De Divina Proportione, 1509.
It is the simplest of five regular polyhedral compounds, and the only regular polyhedral compound composed of only two polyhedra.
It can be seen as a 3D extension of the hexagram: the hexagram is a two-dimensional shape formed from two overlapping equilateral triangles, centrally symmetric to each other, and in the same way the stellated octahedron can be formed from two centrally symmetric overlapping tetrahedra. This can be generalized to any desired amount of higher dimensions; the four-dimensional equivalent construction is the compound of two 5-cells.