The non-arithmetic cusped hyperbolic 3-orbifold of minimal volume

We show that the 1-cusped quotient of the hyperbolic space H3 by the tetrahedral Coxeter group Γ∗ = [5,3,6] has minimal volume among all nonarithmetic cusped hyperbolic 3-orbifolds, and as such it is uniquely determined. Furthermore, the lattice Γ∗ is incommensurable to any GromovPiatetski-Shapiro type lattice. Our methods have their origin in the work of C. Adams [2,3]. We extend considerably this approach via the geometry of the underlying horoball configuration induced by a cusp.

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