Tetraedric

Tetraedric, sometimes spelled tetrahedral or tetraedral, is an adjective relating to a tetrahedron, a polyhedron with four triangular faces, six edges, and four vertices. The term is used to describe shapes, structures, or coordinate systems that are based on or resemble a tetrahedron. While tetrahedral is the more common modern form in English, tetraedric appears in some older texts and in certain languages.

In geometry, a regular tetrahedron has four congruent triangular faces, all of which are equilateral. It has four vertices and six edges. The dihedral angle between any two adjacent faces is approximately 70.53 degrees. Tetrahedric shapes can also refer to non-regular arrangements that nevertheless exhibit a four-faced, tetrahedron-derived structure.

Applications and contexts where tetraedric concepts appear include finite element methods, where tetrahedral meshes are used to discretize three-dimensional domains; computer graphics and geometric modeling, where tetrahedralization helps in volume rendering and collision detection; and chemistry or crystallography, where molecular geometries around central atoms can adopt tetrahedral coordination, such as methane (CH4). In solid-state chemistry, tetrahedric or tetrahedral coordination is used to describe idealized local arrangements around atoms.

Usage notes: the form tetraedric is less common in contemporary technical writing, where tetrahedral is generally preferred. Nevertheless, tetraedric remains a recognized variant in some disciplines and older literature. See also tetrahedron, tetrahedral geometry, and tetrahedral coordination.