High Quality Content by WIKIPEDIA articles! In mathematics, the Bolza surface is a compact Riemann surface of genus 2 with the highest possible order of the conformal automorphism group in this genus, namely 48.The Bolza surface is a (2,3,8) triangle surface. More specifically, the Fuchsian group defining the Bolza surface is a subgroup of the group generated by reflections in the sides of a hyperbolic triangle with angles More specifically, it is a subgroup of the index-two subgroup of the group of reflections, which consists of products of an even number of reflections, which has an abstract presentation in terms of generators s2,s3,s8 and relations s22 = s33 = s88 = 1 as well as s2s3 = s8. The Fuchsian group defining the Bolza surface is also a subgroup of the (3,3,4) triangle group, which is a subgroup of index 2 in the (2,3,8) triangle group. It is interesting to note that the (2,3,8) group does not have a realisation in terms of a quaternion algebra, but the (3,3,4) group does.

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