higher genus surfaces (genus 2 or greater) admit a metric of negative constant curvature (by the uniformization theorem), and the universal cover of the resulting riemann surface is the hyperbolic plane. the corresponding tiling of the hyperbolic plane has vertex figure 3.8.4.8 (triangle, octagon, square, octagon). if the surface is given the appropriate metric of curvature = −1, the covering map is a local isometry and thus the "abstract" vertex figure is the same. this tiling may be denoted by the wythoff symbol 3 4 | 4, and is depicted on the right.