Up: Polyhedra History Articles

# What are Polyhedra?

A polyhedron is a solid whose sides are formed by flat, polygonal surfaces. Polyhedra are three-dimensional objects -- meaning they have length, width, and height.

### More vocabulary

The flat polygons and the regions they enclose are called the polyhedron's faces.

The line segment where two faces meet is called an edge of the polyhedron.

The point where three or more faces meet is called a vertex.

A polyhedron is called uniform if its faces are all regular polygons and its vertices are all congruent. That means if two triangle, two squares, and a pentagon meet at one vertex, then a triangle, two squares, and a pentagon must meet at every vertex.

A polyhedron is called regular if its faces are all regular polygons, and each face is congruent to the other faces. For example, if the faces of a polyhedron are congruent squares, the polyhedron is regular. Regular polyhedra are uniform, but not vice versa.

include defn of convex?

### Polyhedra, viewed as triangle tilings of the sphere

Within these web pages, you will find information about triangle tilings of the sphere, which give rise to two of the many categories of polyhedra. You can read about the 5 Platonic Solids and the 13 Archimedean Solids.