macbeath surface造句

• Interesting examples are provided by the Bolza surface, Klein quartic, Macbeath surface, First Hurwitz triplet.
• The automorphism group of the Macbeath surface is the simple group PSL ( 2, 8 ), consisting of 504 symmetries.
• Torsion-free normal subgroups of the ( 2, 3, 7 ) triangle group are Fuchsian groups associated with Hurwitz surfaces, such as the Klein quartic, Macbeath surface and First Hurwitz triplet.
• Geometrically, it is the smallest Hurwitz surface ( lowest genus ); the next is the Macbeath surface ( genus 7 ), and the following is the First Hurwitz triplet ( 3 surfaces of genus 14 ).
• A co-compact example is the ( ordinary, rotational ) ( 2, 3, 7 ) triangle group, containing the Fuchsian groups of the Klein quartic and of the Macbeath surface, as well as other Hurwitz groups.