Rhombicface

Rhombicface is a term used in geometry to denote a rhombus-shaped polygonal face of a polyhedron or tiling. By definition, a rhombus is a quadrilateral with all sides equal, so a rhombicface is a four-sided face in which the edges around the face are congruent and the opposite sides are parallel, making the face a parallelogram. The diagonals of a rhombicface are perpendicular and bisect each other, and the area of the face equals half the product of its diagonals.

Rhombicfaces occur prominently in rhombic polyhedra, such as the rhombic dodecahedron, which has 12 congruent rhombic faces, and the rhombic triacontahedron, which has 30 rhombic faces. Many plane tilings also use rhombicfaces; a well-known example is the rhombille tiling, in which the plane is covered by congruent rhombuses. In crystallography and materials science, rhombic geometry appears in certain tiling models and grain-boundary representations.

Terminology notes: the term rhombicface is not universally standardized, but it is used informally to describe rhombus-shaped faces in polyhedral and tiling contexts. It can also be written as rhombic face. When precise naming is required, it is common to describe the face by its polygon type (a rhombus-shaped face) and by the polyhedron or tiling in which it appears.

See also: rhombus, parallelogram, rhombic dodecahedron, rhombic triacontahedron, rhombille tiling.