The cusped hyperbolic orbifolds of minimal volume in dimensions less than ten

We detect the cusped complete hyperbolic orbifolds of minimal volume in dimensions less than ten. Our method is geometric and uses results from crystallography and the theory of sphere packings. In fact, such an n-orbifold gives rise to a horoball packing whose orthogonal projection to the cusp boundary yields the densest euclidean lattice packing in dimension n−1.