  Color codes are topological stabilizer codes with unusual transversality
properties. Here I show that their group of transversal gates is optimal and
only depends on the spatial dimension, not the local geometry. I also introduce
a generalized, subsystem version of color codes. In 3D they allow the
transversal implementation of a universal set of gates by gauge fixing, while
error-detecting measurements involve only 4 or 6 qubits.
