An equivalent statement is the following : any centrally symmetric convex body in \ mathbf { R } ^ n has a linear image which contains the unit cross-polytope ( the unit ball for the \ ell _ 1 ^ n norm ) and is contained in the unit cube ( the unit ball for the \ ell _ { \ infty } ^ n norm ).
32.
:My previous comment wasn't about the " number " of points ( indeed, in the continuous limit, \ left ] 0, 1 \ right [ ^ 3 has just as many points as \ mathbb { R } ^ 3 ), but about the restrictions placed on R _ { pq } and x _ { pq } by the requirement that both p and q must lie within the unit cube.
