  We study a 3D generalization of the toric code model introduced recently by
Chamon. This is an exactly solvable spin model with six-qubit nearest neighbor
interactions on an FCC lattice whose ground space exhibits topological quantum
order. The elementary excitations of this model which we call monopoles can be
geometrically described as the corners of rectangular-shaped membranes. We
prove that the creation of an isolated monopole separated from other monopoles
by a distance R requires an operator acting on at least R^2 qubits. Composite
particles that consist of two monopoles (dipoles) and four monopoles
(quadrupoles) can be described as end-points of strings. The peculiar feature
of the model is that dipole-type strings are rigid, that is, such strings must
be aligned with face-diagonals of the lattice. For periodic boundary conditions
the ground space can encode 4g qubits where g is the greatest common divisor of
the lattice dimensions. We describe a complete set of logical operators acting
on the encoded qubits in terms of closed strings and closed membranes.
