  We propose a general approach to analyse diagonal ordering patterns in
bosonic lattice models with algebraically decaying density-density interactions
on arbitrary lattices. The key idea is a systematic search for the
energetically best order on all unit cells of the lattice up to a given extent.
Using resummed couplings we evaluate the energy of the ordering patterns in the
thermodynamic limit using finite unit cells. We apply the proposed approach to
the atomic limit of the extended Bose-Hubbard model on the triangular lattice
at fillings $f=1/2$ and $f=1$. We investigate the ground-state properties of
the antiferromagnetic long-range Ising model on the triangular lattice and
determine a six-fold degenerate plain-stripe phase to be the ground state for
finite decay exponents. We also probe the classical limit of the
Fendley-Sengupta-Sachdev model describing Rydberg atom arrays. We focus on
arrangements where the atoms are placed on the sites or links of the Kagome
lattice. \changed{Our method provides a general framework to treat cristalline
structures resulting from long-range interactions.
