icosohedrons

An icosohedron is a polyhedron with twenty faces. The most common and well-known type is the regular icosohedron, which is one of the five Platonic solids. A regular icosohedron has twenty identical equilateral triangular faces, thirty edges, and twelve vertices. At each vertex, five faces meet. The regular icosohedron possesses a high degree of symmetry.

The term "icosohedron" can also refer to any polyhedron with twenty faces, not necessarily regular. These are called irregular icosohedrons. The shape of the faces and how they connect can vary greatly, leading to many different possible icosohedrons. For example, a bipyramid with a decagonal base would have twenty triangular faces and is a type of icosohedron.

In geometry, icosohedrons appear in various contexts. They are fundamental shapes in the study of polyhedra and crystallography. In chemistry, the icosohedral structure is observed in some molecular arrangements, such as fullerenes (like C60, buckyballs) which have an icosohedral symmetry. The regular icosohedron is also a common shape in dice, particularly in games and role-playing. Its uniform faces ensure a fair roll. The dual of an icosohedron is a dodecahedron.