A polyhedron is a 3-dimensional shape with sides made of polygons. The simplest polyhedron is the tetrahedron, a four sided figure with each side a triangle. A regular tetrahedron has sides that are equilateral triangles. Polyhedra may be concave or convex. The word polyhedron is from the Greek poly (many) and the Indo-European hedron (seat or face).
Each polyhedron contains faces, edges, and vertices. A face of a polyhedron is a polygon, a flat, 2-dimensional shape that make up the boundary of the polyhedron. An edge is where 2 faces join. A vertex of a polyhedron is where two or more edges meet.The Euler-Descarte polyhedron formula relates the number of faces, edges and vertices of convex polyhedra:
V + F - E = 2In the Euler-Descartes formula, V is the number of vertices, F is the number of faces, and E is the number of edges.
Polyhedra are named for the number of sides they possess and, sometimes, the shape of the faces. However, there may be than one shape that qualifies for each name. Click on the name in the table to find out more about that class of polyhedra.
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