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Every affine projection has point symmetry

Source: ICMC 2022 Round 2 P3

March 1, 2022
ICMCgeometrycombinatorial geometry3D geometrycollege contestssymmetry

Problem Statement

A set of points has point symmetry if a reflection in some point maps the set to itself. Let P\cal P be a solid convex polyhedron whose orthogonal projections onto any plane have point symmetry. Prove that P\cal P has point symmetry.
Proposed by Ethan Tan
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