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sum of angles of polyline ABC on surface of cube 1985 Kyiv City MO 10.2

Source:

July 15, 2021
geometry3D geometrycubeangles

Problem Statement

Segment ABAB on the surface of the cube is the shortest polyline on the surface that connects AA and BB. Triangle ABCABC consisted of such segments AB,BC,CAAB, BC,CA. What may be the sum of angles of such triangle if none of the vertex is on the edge of the cube ?
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