tetraeedril

Tetraeedril is a term that appears only sporadically in informal discussions of geometry and world-building, and it is not a standard name for any particular polyhedron in formal mathematical literature. The word seems to derive from combining the prefix tetra-, meaning four, with a suffix echoing -hedron, the common ending for polyhedral names, but there is no universal definition associated with it.

In the few sources that use the term, tetraeedril is sometimes described as a four-faced polyhedron with certain symmetry or congruence properties, distinct from the regular tetrahedron. Some authors treat it as a placeholder label for a hypothetical four-faced solid considered in thought experiments or recreational problems. Because there is no widely accepted definition, different authors may propose different collections of faces, edge relations, and symmetries under the same name.

As a consequence, there is no canonical set of properties that define a tetraeedril. In practice, readers encountering the term should seek the context in which it is introduced to understand what is being described. The term is more likely to appear in informal essays, speculative geometry discussions, or fictional world-building than in standard geometry texts.

Related topics include tetrahedron, disphenoid tetrahedron (a four-faced tetrahedron with congruent faces), and the general study of polyhedra.