Hulek, K. Elliptic curves, abelian surfaces and the icosahedron. (Elliptische Kurven, abelsche Flächen und das Ikosaeder.) (German) Zbl 0704.52005 Jahresber. Dtsch. Math.-Ver. 91, No. 3, 126-147 (1989). Here is mainly given an overview of many results concerning relationships between elliptic curves, abelian surfaces and the icosahedron. Note, that the known discovery of crystallographs obtaining man-made alloys with quasi-crystal structure and icosahedral symmetries in particular intensifies the interest in such investigations. Reviewer: V.F.Ignatenko Cited in 2 Documents MSC: 52B15 Symmetry properties of polytopes 14H52 Elliptic curves 14K05 Algebraic theory of abelian varieties 51M20 Polyhedra and polytopes; regular figures, division of spaces 82D25 Statistical mechanics of crystals Keywords:elliptic curves; abelian surfaces; icosahedron; crystallographs; icosahedral symmetries PDF BibTeX XML Cite \textit{K. Hulek}, Jahresber. Dtsch. Math.-Ver. 91, No. 3, 126--147 (1989; Zbl 0704.52005) OpenURL