rhomboedri

Rhomboedri is the plural form used in some texts for rhombohedra or rhombohedrons, a class of three-dimensional shapes in geometry. In modern English, the more common plurals are rhombohedra or rhombohedrons, but rhomboedri appears in older literature or in certain languages.

A rhombohedron is a polyhedron with six faces, each of which is a rhombus. It is a type of parallelepiped, meaning its faces come in parallel pairs. The three edge directions meet at a vertex and all three edge lengths are equal in a true rhombohedron, ensuring all faces are rhombi. The shape can be viewed as a cube that has been sheared along its axes without changing edge length.

Key properties include the six rhombic faces, three pairs of parallel faces, and the general ability to be described by three edge vectors. The volume of a rhombohedron is given by the absolute value of the scalar triple product of its edge vectors, V = |a · (b × c)|. If the three edges have equal length and non-right mutual angles, the figure remains a rhombohedron, illustrating how deviation from orthogonality introduces rhombic faces while preserving equal edge lengths.

In crystallography, rhombohedra describe the rhombohedral lattice system. The primitive cell in this system is a rhombohedron, though crystals of this system are often represented in a hexagonal or trigonal setting for convenience. The term helps distinguish the three-dimensional rhombic geometry from two-dimensional rhombus shapes.

See also: rhombohedron, rhombohedral lattice, parallelepiped.