page_title: Rhombohedron
section_title: Special cases by symmetry
hierarchical_section_title: Rhombohedron / Special cases by symmetry
context_page_description: In geometry, a rhombohedron is a three-dimensional figure like a cuboid, except that its faces are not rectangles but 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.
  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.
context_section_description: Cube: with Oₕ symmetry, order 48. All faces are squares.
  Trigonal trapezohedron (also called isohedral rhombohedron, or rhombic hexahedron): with D3d symmetry, order 12. All non-obtuse internal angles of the faces are equal (all faces are congruent rhombi). This can be seen by stretching a cube on its body-diagonal axis. For example, a regular octahedron with two regular tetrahedra attached on opposite faces constructs a 60 degree trigonal trapezohedron.
  Right rhombic prism: with D₂ₕ symmetry, order 8. It is constructed by two rhombi and four squares. This can be seen by stretching a cube on its face-diagonal axis. For example, two right prisms with regular triangular bases attached together makes a 60 degree right rhombic prism.
  Oblique rhombic prism: with C₂ₕ symmetry, order 4. It has only one plane of symmetry, through four vertices, and six rhombic faces.
caption: Special cases of the rhombohedron