Polyhedrons with a property of a parallelopiped
Source: Canadian Mathematical Olympiad - 1980 - Problem 5.
May 16, 2011
geometryperimetergeometry unsolved
Problem Statement
A parallelepiped has the property that all cross sections, which are parallel to any fixed face , have the same perimeter as . Determine whether or not any other polyhedron has this property.Typesetter's Note: I believe that proof of existence or non-existence suffices.