Helly hull of Coxeter-group Cayley graphs

Determine the Helly hull of the standard Cayley graph of a Coxeter group.

Background

Helly hulls provide canonical Helly completions of connected graphs, but the notes do not give a general description for standard Cayley graphs of Coxeter groups.

References

What is the Helly hull of the standard Cayley graph of a Coxeter group?

— Group actions on injective spaces and Helly graphs  (2307.00414 - Haettel, 2023) in Section 14, “Open questions,” item 1