where $e_i\ge 2$ and $f_i\ge 2$ for each $i$. Following Vinberg, we call groups defined by a presentations of the form
where each $R_i(a,b)$ is a cyclically reduced word involving both $a$ and $b$, generalized tetrahedron groups}. These groups appear in many contexts, not least as subgroups of generalized triangle groups. In this paper, we build on previous work to start on a complete classification as to which generalized tetrahedron groups are finite; here we treat the case where at least one of the $f_i$ is greater than three.
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