Thurston 1.2.6 (a)
Julian Rosen created a photo and answer:
Imagine three lines of longitude on a unit sphere (embedded in ℝ3), at angles 0, 2π/3, and 4π/3. Let G be the union of those three lines of longitude. Then G has three-fold rotational symmetry and the set of points in ℝ3 that are distance exactly 14 from G form a genus 2 surface.