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Some metric geometry of the icosahedron

Richard Cushman

Abstract

This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated in [2].

Some metric geometry of the icosahedron

Abstract

This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated in [2].
Paper Structure (3 sections, 53 equations)

This paper contains 3 sections, 53 equations.

Table of Contents

  1. Geometry of the vertices
  2. A Riemann surface associated to $K$
  3. Geodesics, symmetry, and billiard motions