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4.25 polytope
A rational convex polytope (in short "polytope") in R^n is the convex
hull of rational points. It may or may not be bounded.
It is internally realized as a cone in one dimension higher, intersected
with the hyperplane x0=1, we will consider it embedded into the projective
space through R^n -> P R^n, x -> (1,x).
Each polytope is uniquely determined by a minimal set of finitely many
points, which we will refer to as "vertices".
Moreover, a polytope can be represented as a set of points satisfying certain
homogeneous linear inequalities and equalities.
And these are the two main ways of constructing non-trivial polytopes.
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