Topic summary
Icosahedral

Extracted from the Wikipedia article Icosahedron.
Regular icosahedra
There are two objects, one convex and one nonconvex, that can both be referred to as regular icosahedra, characterized by 30 edges and 20 triangular faces. The term "regular icosahedron" generally refers to a convex polyhedron, both a deltahedron and a Platonic solid; it is also called "icosahedron" for a plain term. A non-convex polyhedron version is the great icosahedron, a Kepler–Poinsot polyhedron. Both have icosahedral symmetry.