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A query regarding polytope's faces and vertices


Hi,

I am a new mathematica user and I would like to know whether there is a
standard mathematica command/ script to solve the following problem:

Any n- dimensional polytope is defined by the set of linear inequalities
(faces of the polytope). It is also defined by the the set of vertices.
for example:
x <= a,
y<=b;
x+y <= c;
x>=0;
y>=0

Also with the condition that  0<= a,b <= c, this polytope is defined by the
vertices (0,0), (a,0), (b,0), (a, c-a), (c-b, b).

How can this be generalized to any set of linear inequalities? Could you
please help me solve this?

Thanks a lot,
Nilesh



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