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|Symmetry group||D3d, [2+,6], (2*3), order 12|
|Rotation group||D3, [2,3]+, (223), order 6|
|Dual polyhedron||trigonal antiprism|
Six identical rhombic faces can construct two configurations of trigonal trapezohedra. The acute or prolate form has three acute angle corners of the rhombic faces meeting at the two polar axis vertices. The obtuse or oblate or flat form has three obtuse angle corners of the rhombic faces meeting at the two polar axis vertices.
Trigonal trapezohedra are a special kind of parallelepipeds, and are the only parallelepipeds with six congruent faces. Since all edges must have the same length, every trigonal trapezohedron is also a rhombohedron.
A trigonal trapezohedron with square faces is a cube.
A rhombic dodecahedron can be dissected into 4 identical obtuse trigonal trapezohedra.
The rhombic hexecontahedron can be dissected into 20 acute golden rhombohedra meeting at a center point.
The golden rhombohedra are the two special cases of the trigonal trapezohedron with golden rhombus faces. The acute or prolate form has three acute angle corners of the rhombic faces meeting at the two polar axis vertices. The obtuse or oblate or flat form has three obtuse angle corners of the rhombic faces meeting at the two polar axis vertices.
A lower symmetry variation of the trigonal trapezohedron has only rotational symmetry, D3, and is made from 6 identical irregular quadrilaterals. These quadrilaterals necessarily have two adjacent sides of equal length.
|Family of trapezohedra V.n.3.3.3|
- Lines, L (1965). Solid geometry: with chapters on space-lattices, sphere-packs and crystals. Dover Publications.
- Fair Dice: Trigonal Trapezohedron Asymmetrical sides