  We study a model for itinerant, strongly interacting fermions where a
judicious tuning of the interactions leads to a supersymmetric Hamiltonian. On
the triangular lattice this model is known to exhibit a property called
superfrustration, which is characterized by an extensive ground state entropy.
Using a combination of numerical and analytical methods we study various ladder
geometries obtained by imposing doubly periodic boundary conditions on the
triangular lattice. We compare our results to various bounds on the ground
state degeneracy obtained in the literature. For all systems we find that the
number of ground states grows exponentially with system size. For two of the
models that we study we obtain the exact number of ground states by solving the
cohomology problem. For one of these, we find that via a sequence of mappings
the entire spectrum can be understood. It exhibits a gapped phase at 1/4
filling and a gapless phase at 1/6 filling and phase separation at intermediate
fillings. The gapless phase separates into an exponential number of sectors,
where the continuum limit of each sector is described by a superconformal field
theory.
