  We introduce exactly solvable models of interacting (Majorana) fermions in $d
\ge 3$ spatial dimensions that realize a new kind of topological quantum order,
building on a model presented in ref. [1]. These models have extensive
topological ground-state degeneracy and a hierarchy of point-like, topological
excitations that are only free to move within sub-manifolds of the lattice. In
particular, one of our models has fundamental excitations that are completely
stationary. To demonstrate these results, we introduce a powerful polynomial
representation of commuting Majorana Hamiltonians. Remarkably, the physical
properties of the topologically-ordered state are encoded in an algebraic
variety, defined by the common zeros of a set of polynomials over a finite
field. This provides a "geometric" framework for the emergence of topological
order.
