icosaedron

An icosahedron is a polyhedron with twenty faces. The most common type of icosahedron is the regular icosahedron, which is one of the five Platonic solids. A regular icosahedron has twenty equilateral triangle faces, thirty edges, and twelve vertices. At each vertex, five faces meet. It is the dual of the dodecahedron, meaning that if you place a vertex at the center of each face of an icosahedron and connect these vertices, you form a dodecahedron, and vice versa.

The word "icosahedron" comes from the Greek words "eikosi" meaning twenty and "hedra" meaning seat or face. Regular icosahedra are highly symmetric, possessing rotational symmetry and reflectional symmetry. They can be found in nature, for example, in the capsid structures of some viruses. In mathematics, icosahedra appear in various contexts, including geometry and crystallography.

There are also non-regular icosahedra, which have twenty faces but these faces are not all identical equilateral triangles. These can be created by distorting a regular icosahedron or by constructing polyhedra with twenty faces through other means. However, when "icosahedron" is used without qualification, it typically refers to the regular icosahedron.