  We argue that the Weyl coordinates and the rod-structure employed to
construct static axisymmetric solutions in higher dimensional Einstein gravity
can be generalized to the Einstein-Gauss-Bonnet theory. As a concrete
application of the general formalism, we present numerical evidence for the
existence of static black ring solutions in Einstein-Gauss-Bonnet theory in
five spacetime dimensions. They approach asymptotically the Minkowski
background and are supported against collapse by a conical singularity in the
form of a disk. An interesting feature of these solutions is that the
Gauss-Bonnet term reduces the conical excess of the static black rings.
Analogous to the Einstein-Gauss-Bonnet black strings, for a given mass the
static black rings exist up to a maximal value of the Gauss-Bonnet coupling
constant $\alpha'$. Moreover, in the limit of large ring radius, the suitably
rescaled black ring maximal value of $\alpha'$ and the black string maximal
value of $\alpha'$ agree.
