The Klein quartic is tiled regularly by irregular heptagons. Topologically it is a three holed (genus 3) oriented surface, and hence it has a hyperbolic geometry. It has interesting symmetries. Tiling the Poincare disc with the heptagons we see a central heptagon with seven surrounding ones. By following the tiling outwards we generate the sequence 7,7,14,21,35,56,91,147,238, ... which is precisely seven times the Fibonacci sequence! If the three holed surface is squished about it can be made to look like a tetrahedron with tubes for edges. Have fun playing.