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For P ⊂ 3 a finite volume geodesic polyhedron, with the property that all interior angles between incident faces are of the form π/mij (mij ≥ 2 an integer), there is a naturally associated Coxeter group ΓP. Furthermore, this Coxeter group is a lattice inside the semi-simple Lie group O+(3, 1) = Isom(3), with fundamental domain the original polyhedron P. In this paper, we provide a procedure for computing the lower algebraic K-theory of the integral group ring of such groups ΓP in terms of the geometry of the polyhedron P. As an ingredient in the computation, we explicitly calculate the K−1 and Wh of the groups Dn and Dn × 3, and we also summarize what is known about the 0.
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