Compound of two tetrahedra
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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, , order 8||D3d, [2+,6], order 12|
Compound of two tetragonal disphenoids in square prism
Compound of two digonal disphenoids
Compound of two
right triangular pyramids in triangular trapezohedron
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.
- 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.
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