Suppose p sub rn is a full dimensional simple polytope and

Question

Math 121c: Topics in Geometric Combinatorics, Spring 2012 Problems-

(a) Suppose P ⊂ Rⁿ is a full dimensional simple polytope, and 0 ∈∫(P). Prove that P^o is a simplicial polytope.

(b) Show explicitly that if P = conv({±e⁽ⁱ⁾}_i=1ⁿ})) where {±e⁽ⁱ⁾}_i=1ⁿ are the standard basis vectors in Rⁿ, then P^o = conv ({x₁, x₂, . . . , x_n}: x_i ∈ {-1, 1} for all i).