monhedral

Monhedral is a term used in geometry and crystallography to describe a geometric solid or crystal form that possesses a single, undivided face. In simpler terms, it is a shape with only one surface. While this might seem counterintuitive for a three-dimensional object, which typically encloses a volume and thus has multiple surfaces defining its boundaries, the concept of a monhedral form is more abstract and often relates to theoretical constructs or specific contexts within mathematical descriptions.

In the realm of polyhedra, which are solids with multiple faces, a monhedral polyhedron is a theoretical object that would have only one face. This concept is generally not realized in Euclidean geometry as a closed, bounded solid with a non-zero volume. However, in certain advanced mathematical discussions, such as those involving topology or abstract spaces, the idea of a single-faced object might be considered.

Crystallography also sometimes employs the term. When referring to crystal habit, which describes the external shape of a crystal, a monhedral form would indicate a crystal that appears to have a single dominant or predominant face. This often occurs when a crystal grows in a way that one face is significantly larger than all others, giving the overall impression of a singular surface. However, even in such cases, the crystal technically still has other faces, albeit much smaller. The term "monhedral" in this context is more of a descriptive approximation of the observed morphology rather than a strict geometric definition of a single-faced solid.