Elliptic curves, abelian surfaces and the icosahedron. (Elliptische Kurven, abelsche Flächen und das Ikosaeder.) (German) Zbl 0704.52005

Hulek, K.

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

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