Definition:Convex Polyhedron

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This page is about Convex Polyhedron. For other uses, see convex.

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.


Definition 4

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

For each face of $P$, plane containing that face does not intersect any other face of $P$.


Also see

  • Results about convex polyhedra can be found here.