rhomboedrinen

A rhombohedron is a polyhedron with six faces, where each face is a rhombus. It is one of the five Platonic solids, characterized by having congruent regular polygonal faces and identical vertices. The rhombohedron is distinct from the cube, though it can be considered a skewed or "stretched" version of one, where all faces remain rhombic rather than square.

The term "rhombohedron" derives from the Greek words *rhombos* (ῥόμβος), meaning "diamond-shaped," and *hedra* (ἕδρα), meaning "seat" or "base," referring to its faces and structure. It is also known as a rhomboid or rhomboidal dodecahedron, though the latter term is more commonly associated with a different polyhedron with 12 faces.

A rhombohedron can be defined mathematically by three vectors in three-dimensional space that originate from a single vertex. These vectors define the edges meeting at that vertex, and the faces are formed by the parallelograms created by pairs of these vectors. The angles between the vectors are typically equal, but they do not need to be 90 degrees, unlike in a cube.

In crystallography, the rhombohedral system describes a type of crystal lattice where the unit cell is a rhombohedron. This system is one of seven crystal systems, characterized by three equal-length axes intersecting at equal angles that are not 90 degrees. Common minerals, such as calcite and hematite, crystallize in this structure.

The rhombohedron is also relevant in geometry and physics, particularly in studies of symmetry and lattice structures. Its properties make it useful in modeling molecular and atomic arrangements in materials science.