  We construct a new class of stationary exact solutions to five-dimensional
Einstein-Gauss-Bonnet gravity. The solutions are based on four-dimensional
self-dual Atiyah-Hitchin geometry. We find analytical solutions to the
five-dimensional metric function that are regular everywhere. We find some
constraints on the possible physical solutions by investigating the solutions
numerically. We also study the behavior of the solutions in the extremal limits
of the Atiyah-Hitchin geometry. In the extremal limits, the Atiyah-Hitchin
metric reduces to a bolt structure and Euclidean Taub-NUT space, respectively.
In these limits, the five-dimensional metric function approaches to a constant
value and infinity, respectively. We find the asymptotic metrics are regular
everywhere.
