  The natural existence of crystalline symmetry in real materials manifests the
importance of understanding crystalline symmetry-protected topological (SPT)
phases, especially for interacting systems. In this paper, we systematically
construct and classify all the crystalline topological superconductors and
insulators in three-dimensional (3D) interacting fermion systems using the
novel concept of topological crystal. The corresponding higher-order
topological surface theory can also be systematically studied via higher-order
bulk-boundary correspondence. In particular, we discover an intriguing fact
that almost all topological crystals with nontrivial 2D block states are
intrinsically interacting topological phases that cannot be realized in any
free-fermion systems. Moreover, the crystalline equivalence principle for 3D
interacting fermionic systems is also verified, with an additional subtle
"twist" on the spin of fermions.
