Stella octangula
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| Stella octangula | |
|---|---|
 |
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| Type | Regular compound |
| Stellation core | Octahedron |
| Convex hull | Cube |
| Index | UC4, W19 |
| Polyhedra | 2 tetrahedra |
| Faces | 8 triangles |
| Edges | 12 |
| Vertices | 8 |
| Dual | Self-dual |
| Symmetry group | octahedral (Oh) |
| Subgroup restricting to one constituent | tetrahedral (Td) |
The stella octangula, also known as the stellated octahedron, Star Tetrahedron, eight-pointed star, or two-dimensionally as the Star of David. It was given its name by Johannes Kepler in 1609, though it was known to earlier geometers. It was first depicted in Pacioli's Divina Proportione, 1509.
It is the simplest of five regular polyhedral compounds.
It can be seen as either a polyhedron compound or a stellation:
As a compound, is constructed as the union of two tetrahedra (a tetrahedron and its counter-tetrahedron). The vertex arrangement of the two tetrahedra is shared by a cube. The intersection of the two tetrahedra form an inner octahedron, which shares the same face-planes as the compound.
It can be seen as an octahedron with tetrahedral pyramids on each face. It has the same topology as the convex Catalan solid, the triakis octahedron, which has much shorter pyramids.
As a stellation, it is the only stellated form of the octahedron. The stellation facets are very simple: 
(See Wenninger model W19)
Contents |
[edit] Merkaba
The Merkaba is thought to be in the form of a stella octangula.
[edit] See also
[edit] References
- Peter R. Cromwell, Polyhedra, Cambridge, 1997.
- Luca Pacioli, De Divina Proportione, 1509.
