1. Show that the cube C2 = {x R2: - c 2. Suppose for any n = 2, 3, . . . , that the

1. Show that the cube C2 = {x ˆˆ R2: - c

2. Suppose for any n = 2, 3, . . . , that the cube Cn-1 Š‚ conv{(±c, ±c,. . . ±)} Š‚ Rn-1. Show that n-dimensional cube Cn Š‚ conv{(±c, ±c;. . . ,±c)} Š‚ Rn.
3. Conclude that the only extreme points of the cube

are the points of the form (±c, ±c, . . .±c).
4. Show that Cn is the convex hull of its extreme points.

-C -c