Every 8 vertices of a 4-dimensional rectilinear drawing contribute at most 13 crossing pairs of hyperedges, and placing vertices on the moment curve or a neighborly polytope achieves 13.
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Maximum Rectilinear Crossing Number of Uniform Hypergraphs
Every 8 vertices of a 4-dimensional rectilinear drawing contribute at most 13 crossing pairs of hyperedges, and placing vertices on the moment curve or a neighborly polytope achieves 13.