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# 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.