monohédral

Monohédral is a term found in some French-language mathematical and crystallographic literature. It denotes objects that are characterized by a single form or by a single type of face. In English, the corresponding terms are monohedral (for polyhedra whose faces are all the same) or monhedral (relating to a single crystal form). Monohédral usage is not standardized in English-language sources and may appear in translations or in older texts.

In geometry, a monohédral object may refer to a monohedral polyhedron, a solid whose faces are all congruent to one another. In crystallography, monohédral crystals are those whose external morphology is governed by a single crystal form, as opposed to polyhedral crystals that show multiple crystal faces of different forms. The concept is closely related to monohedral tilings, where a single prototile forms the entire tiling.

Etymology: monohédral is built from Greek roots mono- meaning one and hédra (face), with the French diacritic accent. The English equivalents do not routinely carry the accent.

See also: monohedral, monhedral, polyhedron, crystal form, dihedral angle.

Note: For clear communication, use the English terms monohedral or monhedral in technical writing, and reserve monohédral for French-language texts or historical references.