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min length across all lateral faces of regular hexagonal prism

Source: Spanish Mathematical Olympiad 1972 P3

December 5, 2022
geometry3D geometrygeometric inequalityprism

Problem Statement

Given a regular hexagonal prism. Find a polygonal line that, starting from a vertex of the base, runs through all the lateral faces and ends at the vertex of the face top, located on the same edge as the starting vertex, and has a minimum length.