Helly Coxeter groups

Classify the Coxeter groups that are Helly.

Background

The notes list several classes of Helly groups, while emphasizing that only a limited number of crystallographic and Coxeter examples are known. A complete classification of Helly Coxeter groups is explicitly posed.

References

Which Coxeter groups are Helly?

— Group actions on injective spaces and Helly graphs  (2307.00414 - Haettel, 2023) in Section 14, “Open questions,” item 2