  We show that closed arithmetic hyperbolic n-dimensional orbifolds with larger
and larger volumes give rise to triangulations of the underlying spaces whose
1-skeletons are harder and harder to embed nicely in Euclidean space. To show
this we generalize an inequality of Gromov and Guth to hyperbolic n-orbifolds
and find nearly optimal geodesic triangulations of arithmetic hyperbolic
n-orbifolds.
