A 24-Vertex Triangulation of Real Projective 5-Space
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Statement
How few vertices can a triangulation of have? The paper presents a 6-dimensional centrally symmetric simplicial polytope whose antipodal boundary quotient gives a 24-vertex triangulation, far below previous constructions in the Adiprasito-Avvakumov-Karasev line.
Context
A record, not an endpoint: whether fewer vertices suffice is posed as an open question in the same paper.
Small triangulations of projective spaces are a documented question of combinatorial topology (Adiprasito-Avvakumov-Karasev), specialist but with a real literature.
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The construction reduces to a 240-variable optimization over centrally symmetric point sets on the sphere; "we used Google DeepMind's AlphaEvolve as a way to do black-box optimization and ran a large number of instances" before finding the 48-point configuration the triangulation is built from.
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