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cutting 2 regular polyhedra by a plane, and putting pieces together

Source: Sharygin 2010 Final 10.7

November 25, 2018
geometrypolyhedroncutPlane

Problem Statement

Each of two regular polyhedrons PP and QQ was divided by the plane into two parts. One part of PP was attached to one part of QQ along the dividing plane and formed a regular polyhedron not equal to PP and QQ. How many faces can it have?
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