Let G be the group with 4 generators, each of order 2, such that the product of any 2, say ab, has order 3 (i.e., ababab=e). That is, this is an infinite reflection group with Coxeter diagram a tetrahedron. I am looking for references for this group...



Reference for tetrahedral Coxeter group
In terms of references, it seems there are a number references about the orientation preserving subgroups of these groups and their corresponding 3-dimension orbifolds. 


Here are some:


Maclachlan and Reid's "[The Arithmetic of Hyperbolic 3-Manifolds](https://doi.org/10.1007/978-1-4757-6720-9)" has the hyperbolic tetrahedral groups arranged into commensurability classes in the Appendix (Chapter 13) and a longer discussion of about the groups in section 4.7. 


Representations of the orientation preserving subgroups of these Coxeter groups into $PSL(2,\mathbb{C})$ as computed by Grant Lakeland are available in [Matrix Realizations of the Hyperbolic Tetrahedral Groups in ${PSL}\_2(\mathbb C)$](https://www.ux1.eiu.edu/~gslakeland/tetrahedral_realizations.pdf).


The non-hyperbolic examples of these Coxeter groups are classified according to the geometries of their quotients in William Dunbar's paper "[Geometric Orbifolds](https://eudml.org/doc/43193)." 


