A polyhedron is a three dimensional shape bounded by a series of flat planes which are known as faces. A simple example of a polyhedron is a cube, a six-faced polyhedron made with square faces. There is actually some dispute in the math world about what constitutes a polyhedron, exactly, and some mathematical disciplines use the term “polyhedron” to describe a very specific type of shape. For the most part, however, the definition of a three dimensional shape characterized by having flat faces is reasonably accurate.

Each face of a polyhedron is a polygon, another type of geometric figure. Polygons are flat figures made with a series of connecting line segments which form a closed shape. A rectangle is a simple polygon created with four line segments, with a star being a more complex example of a polygon. The polygons in a polyhedron can vary in size, shape, and arrangement considerably, and when all of the polygons are identical, the resulting polyhedron is known as a “symmetrical polyhedron.”

As a general rule, a polyhedron is named according to the number of faces it has. An octahedron has eight faces, a dodecahedron has 12, and so forth. Sometimes, descriptive terms about the shape of the polyhedron will be added as well. A pyramid, for example, is a special type of four or five sided polyhedron. Stellated polyhedrons have numerous pyramidal outcroppings called stellations which create a series of points, causing the polyhedron to take on a three-dimensional star shape.

Polyhedra can be convex, which means that a line drawn between any two points on the shape will pass through the shape without straying beyond its boundaries, or nonconvex, in which the line passes outside the polyhedron. A rectangular block is an example of a convex polyhedron: if you draw an imaginary line between any two points on the block, it will pass through the block. By contrast, a stellated polyhedron is nonconvex, because points which go outside the body of the polyhedron can be drawn between the stellations.

People interact with polyhedrons every day, and the study of polyhedra is critical to a wide variety of industries. For example, many products are packaged in polyhedral containers, with the containers being designed for optimum manufacturing efficiency and stackability. Many homes are polyhedra, created with a series of flat planes which have been used to create an enclosed space. The study of polyhedra tends to be introduced to children at a young age, since understanding polyhedra can be key to grasping other mathematical concepts.