Asymptotic rarity of flag and quadratic triangulations

Determine whether the proportion of d-dimensional (0,1)-equivalence classes admitting a flag unimodular triangulation among those admitting a unimodular triangulation tends to zero, and whether the proportion admitting a quadratic triangulation among those admitting a flag unimodular triangulation tends to zero, as d tends to infinity.

Background

The paper proves that normality and several triangulation properties are rare among all (0,1)-polytopes as the dimension grows. This problem asks for the stronger conditional asymptotics within the subclass of polytopes that already admit unimodular triangulations.

References

Do \frac{fu_d}{u_d}\longrightarrow0 \qquad\text{and}\qquad \frac{q_d}{fu_d}\longrightarrow0?

— Most $(0,1)$-polytopes are not normal  (2609.02778 - Morales, 2 Sep 2026) in Problem Typical triangulable (0,1)-polytopes, Section 5, Open problems