Show that there is no polyhedron with exactly $11$ faces such that each face is a polygon having an odd number of sides.
2026-03-30 11:33:53.1774870433
Polyhedron with $11$ faces
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Twice the number of edges of a polyhedron is the sum of the number of sides of each face. If you have $11$ faces and each face has an odd number of sides, the sum of the number of sides of the faces is odd. Twice the number of edges is even. Contradiction.