Octahedral Symmetry of The Bolza Surface
In Riemann surface theory, the Bolza surface, sometimes called the Bolza curve, is obtained as the ramified double cover of the Riemann sphere, with ramification locus at the set of vertices of the regular inscribed octahedron. Its automorphism group includes the hyperelliptic involution which flips the two sheets of the cover. The quotient by the order 2 subgroup generated by the hyperelliptic involution yields precisely the group of symmetries of the octahedron. Among the many remarkable properties of the Bolza surface is the fact that it maximizes the systole among all genus 2 hyperbolic surfaces.
Read more about this topic: Octahedral Symmetry
Famous quotes containing the words symmetry and/or surface:
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (1788–1824)
“A society which allows an abominable event to burgeon from its dungheap and grow on its surface is like a man who lets a fly crawl unheeded across his face or saliva dribble unstemmed from his mouth—either epileptic or dead.”
—Jean Baudrillard (b. 1929)