deltohedron

Deltohedron, or deltoidal polyhedron, is a polyhedron whose faces are kite-shaped quadrilaterals called deltoids. The name comes from the Greek deltoid, meaning kite. In convex geometry, deltohedra that possess a high degree of symmetry are Catalan solids, the duals of the Archimedean solids. The faces of these solids are congruent deltoids arranged in a uniform pattern.

Two well-known convex deltohedra are the deltoidal icositetrahedron and the deltoidal hexecontahedron. The deltoidal icositetrahedron has 24 kite faces and is the dual of the rhombicuboctahedron; it exhibits octahedral symmetry. The deltoidal hexecontahedron has 60 kite faces and is the dual of the truncated icosidodecahedron, also with octahedral symmetry.

Beyond these and other duals of Archimedean solids, the term deltohedron can be used more generally to describe any polyhedron whose faces are deltoids. Such kite-faced polyhedra may be convex or non-convex, regular or irregular, and arise in various geometric constructions and modeling contexts.

In summary, a deltohedron is a kite-faced polyhedron; when highly symmetric and convex, it typically appears as a Catalan solid arising as the dual of an Archimedean solid, with the deltoidal icositetrahedron and the deltoidal hexecontahedron as primary examples.