|

# polyhedron

polyhedron (pŏlˌēhēˈdrən) [key], 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 Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

#### See more Encyclopedia articles on: Mathematics

Premium Partner Content

Related content from HighBeam Research on: polyhedron

Polyhedra in Poland (Mathematics Teaching)

Responses to the Nets and Polyhedra Problem (Teaching Children Mathematics)

Nets and Polyhedra (Teaching Children Mathematics)

ENEA ACQUIRES UK DATABASE TECHNOLOGY FIRM POLYHEDRA. (Worldwide Databases)

Pursuing Punctured Polyhedra (Science News)

Research on polyhedron discussed by K. Tokarev and co-researchers. (Journal of Technology)

Additional search results provided by HighBeam Research, LLC. © Copyright 2005. All rights reserved.

# 24 X 7

## Private Tutor

 24 x 7 Tutor Availability Unlimited Online Tutoring 1-on-1 Tutoring

### The Family Education Network

About Infoplease,
Part of Family Education Network