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Discrete and Computational Geometry, WS1516 Exercise Sheet “9”: Convex Polytope

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Discrete and Computational Geometry, WS1516 Exercise Sheet “9”: Convex Polytope

University of Bonn, Department of Computer Science I

• Written solutions have to be prepared until Friday 29th of January, 12:00 pm.

• There is a letterbox in front of Room E.01 in the LBH builiding.

• You may work in groups of at most two participants.

Exercise 17: Dual sets (4 Points)

Let C = conv(X)⊆Rd. Please prove the following

C∗ = \

x∈X

D0(x)−.

(For simplicity, you can assume that C contains the origin 0.)

Exercise 18: Duality of Convex Polytope (4 points) Prove the following:

• The dual of a d-dimensional simple convex polytope is ad-dimensional simplical convex polytope.

• The dual of a d-dimensional cube is a d-dimensional cross-polytope.

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