# Polyhedron

## Polyhedron

A solid bounded on all sides by portions of the plane determined by polygons called faces of the polyhedron.

Cubes, prisms and pyramids are polyhedra.

### Properties

• The surface of a polyhedron is made up of polygons.
• Each edge of a polyhedron is shared by two adjacent faces.
• Each vertex is shared by at least three adjacent faces.
• The area of a polyhedron is the sum of the areas of all its faces.
• The volume of a polyhedron is the measure of the portion of space enclosed by the polyhedron.
• In a polyhedron that can be represented in the plane by a connected graph, Euler’s formula which links the number of vertices V, the number of faces F and the number of edges E , is the following: $$V+F=E+2$$.In the polyhedron below, we have: $$8+6=12+2$$.
• Euler’s formula may not be applied to a polyhedron that is represented in a plane by a disconnected graph:

### Example

• This bipyramid is bounded by 12 isosceles triangles.

• This is a rectangular prism:

• This is a hexagonal pyramid: