Universality of 3-dimensional Delaunay subdivisions

Establish that universality holds for three-dimensional Delaunay subdivisions, i.e., that realization spaces of 3D Delaunay subdivisions exhibit universality phenomena analogous to higher dimensions.

Background

Delaunay triangulations can be interpreted via stereographic projections of inscribed polytopes. Universality in higher dimensions implies substantial complexity for recognition and realization.

The authors report a conjecture that universality already manifests in 3D Delaunay subdivisions, a strong statement with significant implications.

References

Adiprasito, Padrol, and Theran conjecture that universality already holds for $3$-dimensional Delaunay subdivisions.

— The Existential Theory of the Reals as a Complexity Class: A Compendium (2407.18006 - Schaefer et al., 25 Jul 2024) in Compendium — Problem 'Delaunay Triangulation'