What is a Polyhedron?
Simply Explained w/ 14 Examples!

So what is a polyhedron?

Well, that’s exactly what this geometry lesson is all about.

You’re going to learn how to identify them along with all their characteristics, including faces, edges, and vertices.

Here we go!

A polyhedron is a three-dimensional solid that is bounded by polygons called faces.

In fact, the word polyhedron is built from Greek stems and roots: “poly” means many and “hedron” means face.

And just like a polygon, a polyhedron does not have curved or intersecting sides (faces).

Additionally, the edge of a polyhedron is a line segment formed by the intersection of two faces and vertices are points where three or more edges meet. And a polyhedron is regular if all of its faces are congruent (i.e., all of its edges are equal).

In the lesson below, we will identify the five classic regular polyhedra: (Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron)

And discover that there is a special relationship between the number of faces, the number of vertices, and the number of edges.

Euler’s theorem says that the number of faces plus the number of vertices equals the number of edges plus two. You’ll see several examples of these in the video too.

In addition, you learn how to use Euler’s Theorem, or the Polyhedral Formula, as Math is Fun states, to find the unknown number of faces, vertices, or edges for any size polyhedron.

Video – Lesson & Examples

29 min

• Introduction to Polyhedrons
• 00:00:23 – What is a Polyhedron? (Examples #1-7)
• 00:10:38 – How do we classify regular and convex polyhedron? (Examples #8-10)
• Exclusive Content for Member’s Only

• 00:17:16 – Euler’s theorem for finding faces, vertices, and edges (Examples #11-14)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions