  We calculate the topological entanglement entropy (TEE) for a
three-dimensional hyperhoneycomb lattice generalization of Kitaev's honeycomb
lattice spin model. We find that for this model TEE is not directly determined
by the total quantum dimension of the system. This is in contrast to general
two dimensional systems and many three dimensional models, where TEE is related
to the total quantum dimension. Our calculation also provides TEE for a
three-dimensional toric-code-type Hamiltonian that emerges as the effective
low-energy theory for the Kitaev model in a particular limit.
