Amapping f is called affine if it is of the form f(x) = ax+b, where a is a matrix and b is a vector. let p and q be polyhedra in rn and rm, respectively. we say that p and q are isomorphic if there exist affine mappings f : p → q and g : q → p such that g(f(x)) = x for all x ∈ p, and f(g(y)) = y for all y ∈ q. (intuitively, isomorphic polyhedra have the same shape.) if p and q are isomorphic, show that there exists a one-to-one correspondence between their extreme points. in particular, if f and g are as above, show that x is an extreme point of p if and only if f(x) is an extreme point of q.