Frequency of unimodularly triangulable lattice polytopes

Determine whether, for each fixed dimension d at least 3, the limsup as V tends to infinity of the fraction of unimodular-equivalence classes of d-dimensional lattice polytopes of normalized volume at most V that admit a unimodular triangulation is strictly less than one.

Background

This problem reformulates an asymptotic question attributed to Haase, Paffenholz, Piechnik, and Santos. It concerns the density of lattice polytopes admitting unimodular triangulations when dimension is fixed and the volume bound tends to infinity.

References

Does \limsup_{V\to\infty}u(d,V){1/V{(d-1)/(d+1)}}<1?

— Most $(0,1)$-polytopes are not normal  (2609.02778 - Morales, 2 Sep 2026) in Problem Haase--Paffenholz--Piechnik--Santos at the counting scale, Section 5, Open problems