Compound of two tetrahedra
In geometry, a compound of two tetrahedra is constructed by two overlapping tetrahedra, usually implied as regular tetrahedra.
There is only one uniform polyhedral compound, the stellated octahedron, which has octahedral symmetry, order 48. It has a regular octahedron core, and shares the same 8 vertices with the cube.
Lower symmetry constructions
There are lower symmetry variations on this compound, based on lower symmetry forms of the tetrahedron.
- A facetting of a rectangular cuboid, creating compounds of two tetragonal or two rhombic disphenoids, with a bipyramid or rhombic fusil cores. This is first in a set of uniform compound of two antiprisms.
- A facetting of a trigonal trapezohedron creates a compound of two right triangular pyramids with a triangular antiprism core. This is first in a set of compounds of two pyramids positioned as point reflections of each other.
| D4h, [4,2], order 16 | D4, [4], order 8 | D3d, [2+,6], order 12 |
|---|---|---|
| 200px Compound of two tetragonal disphenoids in square prism ß{2,4} or     |
180px Compound of two digonal disphenoids |
 Compound of two right triangular pyramids in triangular trapezohedron |
Other compounds
If two regular tetrahedra are given the same orientation on the 3-fold axis, a different compound is made, with D3h, [3,2] symmetry, order 12.
Other orientations can be chosen as 2 tetrahedra within the compound of five tetrahedra and compound of ten tetrahedra:
References
- Cundy, H. and Rollett, A. Five Tetrahedra in a Dodecahedron. §3.10.8 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 139-141, 1989.
External links
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