Vertices, Edges and Faces

A vertex is a corner.
An edge is a line segment between faces.
A face is a single flat surface.

Let us look more closely at each of those:

Vertices

A vertex (plural: vertices) is a point where two or more line segments meet.

It is a Corner.

This tetrahedron has 4 vertices.

And this pentagon has 5 vertices:

Edges

This Pentagon
Has 5 Edges

For a polygon an edge is a line segment on the boundary joining one vertex (corner point) to another.

This Tetrahedron
Has 6 Edges

For a polyhedron an edge is a line segment where two faces meet.

Faces

A face is any of the individual flat surfaces of a solid object. This tetrahedron has 4 faces (there is one face we can't see)

Sides

"Side" is not a very accurate word, because it can mean:

• An edge of a polygon, or
• A face of a polyhedron

Euler's Formula

Try it on the cube:

A cube has 6 faces, 8 vertices, and 12 edges, so:

6 + 8 − 12 = 2

Try counting them here, remember to count the ones you can't see!