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  • 1 University of Calgary, 2500 University Dr. N.W., Calgary, Alberta, T2N 1N4, Canada
  • 2 University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary
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The Separation Problem, originally posed by K. Bezdek in [1], asks for the minimum number s(O, K) of hyperplanes needed to strictly separate an interior point O in a convex body K from all faces of K. It is conjectured that s(O, K) ≦ 2d in d-dimensional Euclidean space. We prove this conjecture for the class of all totally-sewn neighbourly 4-dimensional polytopes.

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