Rhombohedron

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. It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. 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. It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. In general the rhombohedron can have 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. The rhombohedral lattice system has rhombohedral cells, with 3 pairs of unique rhombic faces: For a unit rhombohedron (side length = 1) whose rhombic acute angle is θ and has one vertex is at the origin (0, 0, 0) with one edge lying along the x-axis the three vectors are The other coordinates can be obtained from vector addition of the 3 direction vectors so that e1 + e2, e1 + e3, e2 + e3, and e1 + e2 + e3. The volume of the rhombohedron whose side length is 'a' is a simplification of the volume of a parallelepiped and is given by As the area of the base is given by a 2 sin ⁡ θ {displaystyle a^{2}sin heta } and it follows that the height of a rhombohedron is given by the volume divided by the area. The height, 'h', is given by