There exist positive constants c(0) and c(1) = c(1)(n) such that for every
0 < epsilon < 1/2 the following holds: Let P be a convex polytope in R " ha
ving N greater than or equal to c(0)"/epsilon vertices x(1) ,..., x(N). The
n there exists a subset A subset of {1 ,..., N}, card(A) greater than or eq
ual to (1 - 2 epsilon )N, such that for all i is an element of A
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Also, if P is a convex polytope in R-n having N greater than or equal to c(
0)"/epsilon facets. Let Hit be the half space determined by the facet Fi, w
hich contains P (i = 1 ,..., N). Then there exists a subset A subset of {1
,..., N}, card(A) greater than or equal to (1 - 2 epsilon )N, such that for
all i is an element ofA.
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