Polyhedron

Examples of polyhedra

Regular tetrahedron (Platonic solid) Small stellated dodecahedron (Kepler–Poinsot polyhedron) Icosidodecahedron (Archimedean solid) Great cubicuboctahedron (Uniform star-polyhedron) Rhombic triacontahedron (Catalan solid) A toroidal polyhedron
Definition	A three-dimensional example of the more general polytope in any number of dimensions.
Characteristics	number of faces, topological classification and Euler characteristic, duality, vertex figures, surface area and volume, lines as in geodesics and diagonals, Dehn invariant, highly symmetrical.
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In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary surface. The terms solid polyhedron and polyhedral surface are commonly used to distinguish the two concepts. Also, the term polyhedron is often used to refer implicitly to the whole structure formed by a solid polyhedron, its polyhedral surface, its faces, its edges, and its vertices.

There are many definitions of polyhedra, not all of which are equivalent. Under any definition, polyhedra are typically understood to generalize two-dimensional polygons and to be the three-dimensional specialization of polytopes (a more general concept in any number of dimensions). Polyhedra have several general characteristics that include the number of faces, topological classification by Euler characteristic, duality, vertex figures, surface area, volume, interior lines, Dehn invariant, and symmetry. A symmetry of a polyhedron means that the polyhedron's appearance is unchanged by the transformation such as rotating and reflecting.

The convex polyhedra are a well defined class of polyhedra with several equivalent standard definitions. Every convex polyhedron is the convex hull of its vertices, and the convex hull of a finite set of points is a polyhedron. Many common families of polyhedra, such as cubes and pyramids, are convex.