Abstract
Recently an algorithm has been constructed that shows the binary icosahedral group together with a -like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code that implements transversally. However, no such code has ever been demonstrated in the literature. We fill this void by constructing a family of distance codes that all implement transversally. A surprising feature of this family is that the codes can be deduced entirely from symmetry considerations that only affords.