The isomorphism problem for Coxeter groups has been reduced to its “reflection preserving version” by B Howlett and the second author. Thus, in order to solve it, it suffices to determine for a given Coxeter system all Coxeter generating sets of which are contained in , the set of reflections of . In this paper, we provide a further reduction: it suffices to determine all Coxeter generating sets which are sharp-angled with respect to .
Added 22 May 2012: The description of Figure 3 in Section 8.1 has been corrected.
"Angle-deformations in Coxeter groups." Algebr. Geom. Topol. 8 (4) 2175 - 2208, 2008. https://doi.org/10.2140/agt.2008.8.2175