deltohedrons

A deltohedron is a polyhedron composed of congruent isosceles triangles that meet in groups of three or more around each vertex. The name "deltohedron" is derived from the Greek letter delta (Δ), as its faces are often triangular. A key characteristic of deltohedra is that all of their faces are identical isosceles triangles.

There are two main types of deltohedra: those with triangular symmetry and those with hexagonal symmetry. Triangular deltohedra have faces that are equilateral triangles, and these are also known as deltahedra. The convex deltahedra are the regular tetrahedron, the triangular bipyramid, the pentagonal bipyramid, the octahedron, the snub disphenoid, and the icosahedron. Non-convex deltahedra also exist.

Hexagonal deltohedra have faces that are isosceles triangles but not equilateral. These polyhedra are less commonly studied than their equilateral-faced counterparts. The structure and properties of deltohedra are a topic within geometry, specifically solid geometry and polyhedral combinatorics. Their study often involves analyzing their symmetry groups, vertex configurations, and surface area to volume ratios.