Rhombohedron
| Rhombohedron | |
|---|---|
 |
|
| Type | Prism |
| Faces | 6 rhombi |
| Edges | 12 |
| Vertices | 8 |
| Symmetry group | Ci, [2+,2+], (1x) |
| Properties | convex, zonohedron |
In geometry, a rhombohedron is a three-dimensional figure like a cube, except that its faces are not squares but rhombi. It is a special case of a parallelepiped where all edges are the same length.
In general the rhombohedron can have three types of rhombus faces in congruent opposite pairs.
If all of the non-obtuse internal angles of the faces are equal (all faces are same), it can be called a trigonal trapezohedron.
Another special case is that, where there is a plane of symmetry through four vertices (with symmetry group C2h), and a special case of that, where there is another plane of symmetry through the other four vertices (with symmetry group D2h).
The cube combines these special properties, and so is a special case of the rhombohedron. A less symmetric example is a rhombic prism, constructed by two rhombi and 4 squares, with D2h symmetry.
The rhombohedral lattice system has rhombohedral cells, with 3 pairs of unique rhombic faces:
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