Hands-on math!

Polyhedron

A polyhedron is a 3-dimensional (solid) figure with flat faces. Cubes and pyramids are polyhedrons. Each flat face is a polygon. A polyhedron where all the faces are the same (congruent) is a regular polyhedron.
There are only 5 regular polyhedrons. Here are all of the regular polyhedrons:

tetrahedron
   
cube
   
octahedron
   
icosahedron
   
dodecahedron

Here are the volumes and surface areas of the regular polyhedrons: (s is the length of a side)
 
  Surface areaVolume
ExactApproximateExactApproximate

tetrahedron
(√3) s2  (1.732) s2
s32
12
(0.11785) s3

cube
6 s2 s3  

octahedron
(2√3) s2  (3.464) s2
s32
3
(0.4714) s3

icosahedron
(5√3) s2  (8.660) s2
s3 (15 + 5√5)
12
(2.1817) s3

dodecahedron
s2 (3√25+10√5 ) (20.64558) s2
s3 (15 + 7√5)
4
(7.6631) s3