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Trigonal trapezohedron
| Trigonal trapezohedron | |
|---|---|
| |
| Type | trapezohedron |
| Conway notation | dA3 |
| Coxeter diagram |     
|
| Faces | 6 rhombi |
| Edges | 12 |
| Vertices | 8 |
| Face configuration | 3,3,3,3 |
| Symmetry group | D3d, [2+,6], (2*3), order 12 |
| Rotation group | D3, [2,3]+, (223), order 6 |
| Dual polyhedron | trigonal antiprism |
| Properties | convex, equilateral polygon, face-transitive, zonohedron, parallelohedron |
In geometry, a trigonal trapezohedron is a polyhedron with six congruent quadrilateral faces, which may be scalene or rhomboid.[1][2] The variety with rhombus-shaped faces faces is a rhombohedron.[3][4] An alternative name for the same shape is the trigonal deltohedron.[5]
- ^ Cromwell, P.Polyhedra, ppbk CUP 1999, pp.302,304,367.
- ^ Cundy & Rollett (p.117).
- ^ Lines, L (1965). Solid geometry: with chapters on space-lattices, sphere-packs and crystals. Dover Publications.
- ^ Grünbaum, Branko (2010). "The Bilinski dodecahedron and assorted parallelohedra, zonohedra, monohedra, isozonohedra, and otherhedra". The Mathematical Intelligencer. 32 (4): 5–15. doi:10.1007/s00283-010-9138-7. hdl:1773/15593. MR 2747698.
- ^ Futamura, F.; Frantz, M.; Crannell, A. (2014). "The cross ratio as a shape parameter for Dürer's solid". Journal of Mathematics and the Arts. 8 (3–4): 111–119. doi:10.1080/17513472.2014.974483. MR 3292158.
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