disphenohedral

Disphenohedral is a geometric term used to describe figures whose faces are congruent triangles, most often referring to a disphenoid or disphenohedron. The best-known example is the disphenoid tetrahedron, also called an equifacial tetrahedron, which has four congruent triangular faces.

In a disphenoid tetrahedron, all faces are congruent, and the three pairs of opposite edges are equal in length. The shape exhibits a distinct but non-regular symmetry: its symmetry group is generally described as D2d, featuring three two-fold axes and mirror planes. These properties make the disphenoid tetrahedron an interesting case among tetrahedra, lying between the regular tetrahedron and a generic scalene one in terms of symmetry and edge relations.

More broadly, disphenohedral can describe any polyhedron whose faces are congruent triangles, not limited to tetrahedra. Such figures are sometimes discussed in crystallography, tiling theory, and architectural geometry, where sets of congruent triangular faces can organize into space-filling cells or symmetric assemblies.

Summary: Disphenohedral refers to the class of shapes characterized by congruent triangular faces, with the disphenoid tetrahedron serving as the principal and most familiar example. The term captures both a specific tetrahedral instance and a broader property applicable to other congruent-triangle polyhedra. See also disphenoid and disphenohedron.