Abstract
Two pairs (A,B),(C,D) of compact convex sets are equivalent if A + D = B + C, where ‘+’ is the Minkowski sum. In 15, the question was posed whether two equivalent minimal pairs are translates of each other. In 6, the first example of a three-dimensional minimal pair, which has an equivalent minimal pair not being the translate of the former, was given. Incidentally, the Minkowski sum of that pair resembles the famous polyhedron from Dürer's ‘Melancholy’. In this article, we give the decomposition of the polyhedron to a minimal pair of compact convex sets and prove that this pair belongs to a quotient class without the property of translation. †Dedicated to H. Th. Jongen on the occasion of his 60th birthday.
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