We construct a fundamental domain ω for an arbitrary lattice [unk] in a real rank one, real simple Lie group, where ω has finitely many cusps (i.e., is a finite union of Siegel sets) and has the Siegel property (i.e., the set {γ [unk] [unk]|ωγ [unk] ω [unk] ϕ} is finite). From the existence of ω we derive a number of consequences. In particular, we show that [unk] is finitely presentable and is almost always rigid.
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