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coloring a polyhedron

Source: Brazil TST 1999 Test 2 P4

April 30, 2021
geometry3D geometry

Problem Statement

Assume that it is possible to color more than half of the surfaces of a given polyhedron so that no two colored surfaces have a common edge.
(a) Describe one polyhedron with the above property. (b) Prove that one cannot inscribe a sphere touching all the surfaces of a polyhedron with the above property.