The method used to calculate the volume of each elemental pyramid is based on a calculation of the

convex polyhedron volume [23].

The line of sight checking algorithm considers an obstacle as a

convex polyhedron [OMEGA] consisting a set of convex polygon faces [F.sub.i] where i is a polygon face.

We call F = {[C.sub.1], ..., [C.sub.m]} a convex polyhedral fan for P if P [intersection] [C.sub.j] is for every j, j [member of] {1, ..., m} a

convex polyhedron. Due to the considerations of convex polyhedra in the broad literature of convex geometry, it is possible to represent a

convex polyhedron in two different but equivalent ways; see [24].

We call F a convex fundamental polyhedron, if F is a fundamental domain that is a

convex polyhedron. The group [GAMMA] is said to be cofinite if F has finite volume.

This is based on enclosing a

convex polyhedron in a sphere; it is usually called the outer sphere (Hubbard, 1996; Pitt-Francis, 1998; James & Pai, 2004).

The convex hull of a set of points in 3D is the smallest

convex polyhedron enclosing all the input points.

The natural generalization of the process of rotating a line constrained to remain tangent to a convex polygon in two dimensions, to 3-dimensional space, is rotating a plane that remains tangent to a

convex polyhedron. To specify the direction of rotation uniquely the plane should be tangent to two points in space, which determine the axis of rotation of the plane.

Instead they claimed to have found a way of making those angles zero, which makes all the faces flat, and what is left is a true

convex polyhedron .

If X is a

convex polyhedron, then the convex optimization problem (16) is a semidefinite program that can be solved by SeDuMi conic optimizer.

Considering that the upper bound depends on the two time-varying delays, we propose the so-called

convex polyhedron method to check the negative definiteness for it.

An efficient way to detect if a point is inside a

convex polyhedron was presented in He (2010).

Students can identify all the centres of the cube faces step by step and then plot a

convex polyhedron with its vertices being constituted by the centers of the cube faces.