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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Schulte et al. (1985) studied this question.