Counting Faces, Edges & Vertices of Polyhedrons

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  • 0:00 Polyhedrons
  • 0:40 Counting Faces
  • 1:00 Counting Edges
  • 1:05 Counting Vertices
  • 1:15 The Relationship
  • 3:10 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to count how many faces, edges, and vertices a polyhedron has. Also, you will learn how the number of faces, edges, and vertices are related.

A Polyhedron

In this lesson, we will talk about polyhedrons and how to count the number of faces, edges, and vertices they have. A polyhedron is a three-dimensional solid with straight edges and flat sides. The faces of a polyhedron are its flat sides. The edges of a polyhedron are the edges where the faces meet each other. The vertices are the corners of the polyhedron.

Knowing how to count the number of faces, edges, and vertices of a polyhedron will serve you well as you progress in your math classes. So, let's explore counting the faces, edges, and vertices of this polyhedron:


In this polyhedron, I've also marked what a face is, what an edge is, and what a vertex is. So, let's see how to count the number of faces, edges, and vertices.

Counting Faces

So to count the number of faces, you look for how many flat sides the polyhedron has. Looking at the shape, you see that it has a face on top, on the bottom, to the left and to the right, on the front and at the back. Counting each of these, you end up with 6 faces. So, this polyhedron has 6 faces.

Counting Edges

Now let's count the edges of the polyhedron. You see that it has four edges around the top face and four edges around the bottom face. Then it has four edges going around the middle of the polyhedron. This makes for 12 edges.

Counting Vertices

As for the vertices, you see that it has four corners on top and four corners on the bottom. This makes for a total of 8 vertices.

The Relationship

These numbers - 6 faces, 12 edges, and 8 vertices - are actually related to each other. This relationship is written as a math formula like this:

F + V - E = 2

This formula is known as Euler's formula. The F stands for faces, the V stands for vertices, and the E stands for edges. It tells us that if we add the number of faces and vertices together and then subtract the number of edges, we will get 2 as our answer.

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