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 area | Volume |
| Exact | Approximate | Exact | Approximate |
tetrahedron |
(√3) s2
| (1.732) s2 |
s3
√2
12 |
(0.11785) s3 |
cube | 6 s2 | | s3 | |
octahedron | (2√3) s2
| (3.464) s2 | s3
√2
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 |
|