  Geometrical Bell Inequalities (GBIs) are the strongest known Bell
inequalities for collections of qubits. However, their generalizations to other
systems is not yet fully understood. We formulate GBIs for an arbitrary number
$N$ of observers, each of which possesses a particle of an arbitrary dimension
$d$. The whole $(d-1)$-parameter family of local observables with eigenbases
unbiased to the computational basis is used, but it is immediate to use a
discrete subset of them. We argue analytically for qutrits and numerically for
other systems that the violations grows exponenetially with $N$. Within the
studied range, the violation also grows with $d$. Interestingly, we observe
that the logarithm of the violation ratio for ququats grows with $N$ slower
than the doubled logarithm of the violation ratio for qubits, which implies a
kind of subadditivity.
