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Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
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Accepted
3-colored triangulations of the sphere $S^2$, and Sperner's Lemma
A counting proof shows that this observation is unrelated to the global topology.
Every edge is monochromatic or dichromatic. How many dichromatic edges are there? If each triangle tells you its num …