All symmetry groups for surfaces of genus 2 and 3 are known. In this paper, we classify symmetry groups and tiling groups with three branch points for surfaces of genus 4 and 5. Also, a class of symmetry groups that are not tiling groups is presented, as well as a class of odd order non-abelian tiling groups.

Author Bio

Ryan received his BS in mathematics from North Carolina StateUniversity in 1998, and is currently in graduate school at Stanford University studying algebraic number theory and elliptic curves. Other than mathematics, hobbies include basketball and playing variouspercussion instruments.