Semistable K3-surfaces with icosahedral symmetry

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In a Type III degeneration of K3-surfaces the dual graph of the central fibre is a triangulation of the 2-sphere. We realise the tetrahedral, octahedral and especially the icosahedral triangulation in families of K3-surfaces, preferably with the associated symmetry groups acting.
31 pages, 7 ps-figures

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