I will review results, obtained with P. Fendley
and L. Huijse, on lattice models for spin-less fermions
with strong repulsive interactions. A judicious tuning
of kinetic and interaction terms leads to a model
possessing supersymmetry. In the 1D case, this model
displays critical behavior described by superconformal
field theory. On 2D lattice we generically find
superfrustration, with ground state entropy that is
extensive in the size of system. For special
2D lattices we observe special features which we
tentatively describe as `supertopological'.
