Solid Geometry: Polyhedrons

Polyhedrons - solids whose faces are plane polygons.

Regular Polyhedrons - are polyhedrons that have identical faces. There are only five known kinds of polyhedrons.

Let:
a = length of the edge
n = number of vertices
f = number of faces
m = number of polygons meeting at a vertex

• Tetrahedron - four faces - a pyramid
• faces: 4
• edges: 6
• vertices: 4
• number of polygons meeting at a vertex: 3
• surface area: a square * square root of 3
• volume: a cube / 6 * square root of 2 

• Hexahedron - six faces - a cube
• faces: 6
• edges: 12
• vertices: 8
• number of polygons meeting at a vertex: 3
• surface area: 6 * a square
• volume: a cube

• Octahedron - eight faces
• faces: 6
• edges: 12
• vertices: 8
• number of polygons meeting at a vertex: 4
• surface area: 6 * a square
• volume: a cube

• Dodecahedron - twelve faces
  • faces: 12
  • edges: 30
  • vertices: 20
  • number of polygons meeting at a vertex: 3

• Icosahedron - twenty faces
• faces: 6
• edges: 12
• vertices: 8
• number of polygons meeting at a vertex: 5

For any Polyhedron:

Number of Edges: nf/2

Number of Vertices: nf/m