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A 24-Vertex Triangulation of Real Projective 5-Space

Geometry & topology · partial

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Statement

How few vertices can a triangulation of RP5\mathbb{RP}^5 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.

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  1. construction · #1

    Dan Guyer, Stefan Steinerberger and Yirong Yang, using AlphaEvolve

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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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