platonic surface
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scholarly journals A new approach to the automorphism group of a platonic surface

2020 ◽  
Vol 50 (1) ◽  
pp. 9-23
Author(s):  
David Aulicino
Keyword(s):  
Automorphism Group ◽  
New Approach ◽  
Platonic Surface

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

2001 ◽  
Vol 33 (6) ◽  
pp. 701-710 ◽  
Author(s):  
DAVID SINGERMAN
Keyword(s):  
Riemann Surface ◽  
Automorphism Group ◽  
Uniqueness Theorem ◽  
Felix Klein ◽  
Platonic Surface ◽  
Hyperbolic Polygon

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.

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