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What is a 'CoxeterGroup'?

Hi, I'm trying to implement a certain Coxeter group in Sage, for the purpose of building the corresponding Iwahori-Hecke algebra over it using sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra. In the documentation of the constructor of this class, it says that it takes a "Coxeter group" as an argument. However, Coxeter groups as generated by sage.combinat.root_system.coxeter_group.CoxeterGroup aren't actually instances of a common superclass.

Afaict, the methods of IwahoriHeckeAlgebra simply implicitly assume the existence of certain instance methods (like W.is_finite or W.from_reduced_word), probably also with some implicitly assumed semantics of said methods. So, my question is whether the behaviour of being a "Coxeter group" are actually anywhere formally documented, or whether I'm stuck piecing together the required methods & semantics through trial and error.