# Definition:Convex Polyhedron

## Definition

Let $P$ be a polyhedron.

### Definition 1

$P$ is a convex polyhedron if and only if:

For all points $A$ and $B$ located inside $P$, the line $AB$ is also inside $P$.

### Definition 2

$P$ is a convex polyhedron if and only if:

For every face of $P$, the plane in which it is embedded does not intersect the interior of $P$.

### Definition 3

$P$ is a convex polyhedron if and only if:

For each face of $P$, the whole of $P$ lies on one side of the plane of that face.

## Also see

• Results about convex polyhedra can be found here.