Skip to main content Skip to Search Box

Definition: polyhedron from Philip's Encyclopedia

In geometry, three-dimensional solid figure whose surface is made up of polygons. The polygons are called the faces of the polyhedron, and the points at which they meet are the vertices.

Summary Article: polyhedron
From The Columbia Encyclopedia

(pŏl´´ēhē'drӘn), closed solid bounded by plane faces; each face of a polyhedron is a polygon. A cube is a polyhedron bounded by six polygons (in this case squares) meeting at right angles. Although regular polygons are possible for any number of sides, there are only five possible regular polyhedrons, having congruent faces, each a regular polygon and meeting at equal angles. The five regular polyhedrons are also known as the Platonic solids, although they were known to the Greeks before the time of Plato. They are the tetrahedron, bounded by four equilateral triangles; the hexahedron, or cube, bounded by six squares; the octahedron, bounded by eight equilateral triangles; the dodecahedron, bounded by twelve regular pentagons; and the icosahedron, bounded by twenty equilateral triangles. The 18th-century Swiss mathematician Leonhard Euler showed that for any simple polyhedron, i.e., a polyhedron containing no holes, the sum of the number of vertices V and the number of faces F is equal to the number of edges E plus 2, or V+F=E+2.

The Columbia Encyclopedia, © Columbia University Press 2018

Related Articles

Full text Article polyhedron(plural polyhedra)
The Penguin Dictionary of Mathematics

1. A solid with a surface composed of plane polygonal surfaces ( faces ). The sides of the polygons, joining two faces, are its edges . The...

Full text Article Platonic solid
Britannica Concise Encyclopedia

Geometric solid all of whose faces are identical regular polygons and all of whose angles are equal. There are only five such polyhedrons. The cube

Full text Article polyhedron
The Hutchinson Unabridged Encyclopedia with Atlas and Weather Guide

In geometry, a solid figure with four or more plane faces. The more faces there are on a polyhedron, the more closely it approximates to a sphere. Kn

See more from Credo