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:
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:|
Has 5 Edges
For a polygon an edge is a line segment on the boundary joining one vertex (corner point) to another.
Has 6 Edges
For a polyhedron an edge is a line segment where two faces meet.
A face is any of the individual flat surfaces of a solid object.
This tetrahedron has 4 faces (there is one face you can't see)
"Side" is not a very accurate word, because it can mean:
- An edge of a polygon, or
- A face of a polyhedron
For many solid shapes the
- Number of Faces
- plus the Number of Vertices
- minus the Number of Edges
always equals 2
This can be written: F + V − E = 2
Try it on the cube:
A cube has 6 Faces, 8 Vertices, and 12 Edges,
6 + 8 − 12 = 2
(To find out more about this read Euler's Formula.)