  Topological crystalline states are short-range entangled states jointly
protected by onsite and crystalline symmetries. While the non-interacting limit
of these states, e.g., the topological crystalline insulators, have been
intensively studied in band theory and have been experimentally discovered, the
classification and diagnosis of their strongly interacting counterparts are
relatively less well understood. Here we present a unified scheme for
constructing all topological crystalline states, bosonic and fermionic, free
and interacting, from real-space "building blocks" and "connectors". Building
blocks are finite-size pieces of lower dimensional topological states protected
by onsite symmetries alone, and connectors are "glue" that complete the open
edges shared by two or multiple pieces of building blocks. The resulted
assemblies are selected against two physical criteria we call the "no-open-edge
condition" and the "bubble equivalence", which, respectively, ensure that each
selected assembly is gapped in the bulk and cannot be deformed to a product
state. The scheme is then applied to obtaining the full classification of
bosonic topological crystalline states protected by several onsite symmetry
groups and each of the 17 wallpaper groups in two dimensions and 230 space
groups in three dimensions. We claim that our real-space recipes give the
complete set of topological crystalline states for bosons and fermions, and
prove the boson case analytically using a spectral sequence expansion of group
cohomology.
