Rhombohedron
In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a three-dimensional figure with six faces which are rhombi. It is a special case of a parallelepiped where all edges are the same length. It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. A cube is a special case of a rhombohedron with all sides square.
| Rhombohedron | |
|---|---|
| Type | prism |
| Faces | 6 rhombi |
| Edges | 12 |
| Vertices | 8 |
| Symmetry group | Ci , [2+,2+], (×), order 2 |
| Properties | convex, equilateral, zonohedron, parallelohedron |
In general a rhombohedron can have up to three types of rhombic faces in congruent opposite pairs, Ci symmetry, order 2.
Four points forming non-adjacent vertices of a rhombohedron necessarily form the four vertices of an orthocentric tetrahedron, and all orthocentric tetrahedra can be formed in this way.
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