  Self-assembly of colloidal particles is poised to become a powerful composite
material fabrication technique, but remains challenged by a limited control
over the ensuing structures. We develop a new breed of nematic colloids that
are physical analogs of a mathematical surface with boundary, interacting with
the molecular alignment field without inducing defects when flat. However, made
from a thin nanofoil, they can be shaped to prompt formation of
self-compensating defects that drive pre-programmed elastic interactions
mediated by the nematic host. To show this, we wrap the nanofoil on all
triangular side faces of a pyramid, except its square base. The ensuing
pyramidal cones induce point defects with fractional hedgehog charges of
opposite signs, spontaneously align with respect to the far-field director to
form elastic dipoles and nested assemblies with tunable spacing. Nanofoils
shaped into octahedrons interact as elastic quadrupoles. Our findings may drive
realization of low-symmetry colloidal phases.
