Problem 3. (Faces of polytopes)
Let n be a natural number. Consider the polytope defined as the convex
hull of the 2n vectors which one gets by taking the standard basis vectors in
Rn together with their negatives:
     
 
±1
0
0
0
 0  ±1  0 
0
     
 
 0   0  ±1
 
  ,   ,   , . . . ,  0  ∈ Rn .
 ..   ..   .. 
 .. 
 .   .   . 
 . 
0
0
±1
0
Determine the complete list of faces and corresponding supporting hyperplanes for this polytope.
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