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Journal of the London Mathematical Society 1985 s2-32(3):539-547; doi:10.1112/jlms/s2-32.3.539
© 1985 by London Mathematical Society
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© Oxford University Press

A Polyhedral Realization of Felix Klein's Map {3, 7}8 on a Riemann Surface of Genus 3

E. Schulte and J. M. Wills

Mathematisches Institut, Universität Dortmund D-4600 Dortmund 50, Federal Republic of Germany
Mathematisches Institut, Universität Siegen Hoelderlinstraße 3, D-5900 Siegen, Federal Republic of Germany

In his famous work on elliptic functions Felix Klein constructed a map on a Riemann surface of genus 3 to illustrate the (simple) transformation group of order 168 for the solution of equations of degree 7. In Coxeter's notation, this map and its dual are {7, 3}8 and {3, 7}8 respectively. We describe a polyhedral realization of {3, 7}8 in Euclidean 3-space, thereby underlining the strong analogy to the significance of the icosahedron for transformations of the quintic equation.


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