  Error bounds are a requisite for trusting or distrusting solutions in an
informed way. Until recently, provable error bounds in the absence of
constraint qualifications were unattainable for many classes of cones that do
not admit projections with known succinct expressions. We build such error
bounds for the generalized power cones, using the recently developed framework
of one-step facial residual functions. We also show that our error bounds are
tight in the sense of that framework. Besides their utility for understanding
solution reliability, the error bounds we discover have additional applications
to the algebraic structure of the underlying cone, which we describe. In
particular we use the error bounds to compute the dimension of the automorphism
group for the generalized power cones, and to identify a set of generalized
power cones that are self-dual, irreducible, nonhomogeneous, and perfect
