Polyhedra
A polyhedron is a figure formed by polygons which enclose a region of $3$ dimensional space.
The polygons are called faces , the line segments in which they intersect are called edges , and the endpoints of the edges are called vertices .
For example, the pyramid shown below has $7$ faces ( $1$ hexagon and $6$ triangles), $12$ edges (six segments converging at the apex, the point where the side faces meet), and $7$ vertices ( $6$ in the base plus the apex).
A regular polyhedron has for its faces all congruent, regular polygons. There are only five regular polyhedrons; they are known as the platonic solids .
Name

Drawing

# of Faces

# of Edges

# of Vertices

Regular Tetrahedron 
$4$

$6$

$4$


Cube 
$6$

$12$

$8$


Regular Octahedron 
$8$

$12$

$6$


Regular Dodecahedron 
$12$

$30$

$20$


Regular Icosahedron 
$20$

$30$

$12$

You may notice that the number of faces plus the number of vertices, minus the number of edges, is always equal to $2$ . This is true for any polyhedron in $3$ dimensional space, and is known as Euler's formula :
$VE+F=2$