Stellated octahedron
| Stella octangula | |
|---|---|
| |
| Type | Stellation and compound |
| Polyhedra | 2 tetrahedra |
| Faces | 8 triangles |
| Edges | 12 |
| Vertices | 8 |
| Dual | Self-dual |
| Symmetry group | octahedral (Oh) |
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. 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)
In modern New Age/esoteric teachings, it is taught that the MerKaBa is an interdimensional vehicle consisting of two equally sized, interlocked tetrahedra of light with a common center, where one tetrahedron points up and the other down.
In his books, researcher and physicist Drunvalo Melchizedek describes this figure as a "Star Tetrahedron", since it can be viewed as a three dimensional Star of David. By imagining two superimposed "Star Tetrahedrons" as counterrotating, along with specific "prana" breathing techniques, certain eye movements and mudras, it is taught that one can activate a non-visible 'saucer' shaped energy field around the human body that is anchored at the base of the spine. Depending on the height of the person doing the exercise, this field is thought to be approximately 55 feet across. Once activated, this 'saucer' shaped field is capable of carrying one's consciousness directly to higher dimensions.
See also
References
- Peter R. Cromwell, Polyhedra, Cambridge, 1997.
- Luca Pacioli, De Divina Proportione, 1509.
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