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UNICELLULAR DESSINS AND A UNIQUENESS THEOREM FOR KLEIN'S RIEMANN SURFACE OF GENUS 3

Published online by Cambridge University Press:  28 November 2001

DAVID SINGERMAN
DAVID SINGERMAN
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton, S017 1BJ; [email protected]
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Abstract

If we consider the 14-sided hyperbolic polygon of Felix Klein that defines his famous surface of genus 3, then we observe that we have a uniform, unifacial dessin whose automorphism group is transitive on the edges, but not on the directed edges of the dessin. We show that Klein's surface is the unique platonic surface with this property.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 6 , November 2001 , pp. 701 - 710
Copyright
© The London Mathematical Society 2001

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