A 24-Vertex Triangulation of Real Projective 5-Space
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.
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Combinatorial topology
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-03-08
- Model
- AlphaEvolve
- Vendor
- Google DeepMind
- Collaborators
- Dan Guyer, Stefan Steinerberger, Yirong Yang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
A record, not an endpoint: whether fewer vertices suffice is posed as an open question in the same paper.
What the AI did
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.