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: [latex]V+F=E+2[/latex].In the polyhedron below, we have: [latex]8+6=12+2[/latex].
- 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:
