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A Polyhedral Realization of Felix Klein's Map {3, 7} 8 on a Riemann Surface of Genus 3
Author(s) -
Schulte E.,
Wills J. M.
Publication year - 1985
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-32.3.539
Subject(s) - riemann surface , genus , coxeter group , mathematics , realization (probability) , quintic function , pure mathematics , surface (topology) , transformation (genetics) , euclidean space , riemann sphere , simple (philosophy) , algebra over a field , geometry , physics , quantum mechanics , biochemistry , statistics , botany , chemistry , epistemology , philosophy , nonlinear system , gene , biology
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.