If all principal congruences of a finite lattice are regular/uniform/isoform, are then all congruences regular/uniform/isoform?
A congruence $\{S_1, \ldots, S_n\}$ is isoform if all congruence blocks are isomorphic; it is uniform if all congruence blocks have equal number of elements; it is regular if the congruence generated by any of $S_i$ is the same. See https://arxiv.org/pdf/1309.7525.pdf for information on those.
A congruence is principal if it is generated by a block of a join-irreducible element and the element covered by it.