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Geometry » Polytopes

Extension complexity of (convex) polygons ★★

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The extension complexity of a polytope $ P $ is the minimum number $ q $ for which there exists a polytope $ Q $ with $ q $ facets and an affine mapping $ \pi $ with $ \pi(Q) = P $.

Question   Does there exists, for infinitely many integers $ n $, a convex polygon on $ n $ vertices whose extension complexity is $ \Omega(n) $?

Keywords: polytope, projection, extension complexity, convex polygon

Posted by DOT
updated August 13th, 2011
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