Given an irreducible graph on a ball (a sphere in three dimensions). The inner angles of a triangle, quadrangle and pentagon are smaller than $180^{\circ}$. Could anybody give a proof of this statement?
2026-05-01 18:58:43.1777661923
Inner angles of an irreducible graph on a sphere
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If this is in relation to your other question, then it seems to me you're dealing with regular polygons, which are of course convex. Otherwise, it would be fairly easy to draw a non-convex quadrilateral on a sphere, where the inner angle at the non-convex corner would exceed $180°$.