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Jul 13, 2019 at 2:53 comment added Ian Agol Any surface is a cyclic cover of genus 2, so maybe a dihedral action?
Jul 12, 2019 at 21:28 comment added Dylan Thurston Can you make a face-transitive tiling by heptagons in every genus? (Or various other regular polygons.)
Jul 11, 2019 at 20:58 comment added Ian Agol As you're probably aware, Michael Larsen has addressed how frequently the Hurwitz bound is achieved. mathscinet.ams.org/mathscinet-getitem?mr=1882031 But one could also just ask for a transitive action on the faces (or on the vertices). Bestvina's example desribed by Christopher is of this type. mathoverflow.net/questions/198040/…
Jul 11, 2019 at 4:00 history answered Dylan Thurston CC BY-SA 4.0