Abstract
2, which was resolved by synthetic methods first by Leonard Euler in 1750. An arbitrary rectangular hexahedron has a quadric as its Fermat locus. This quadric is either an ellipsoid, a rotational paraboloid or a hyperboloid with two sheets. Conversely, for every quadric from any of these three types one can ask to find all of its rectangular hexahedron Fermat bases which share a line of symmetry with the quadric.
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