Higher-dimensional sphere packings, lattices and polytopes. I

Ichiro Takada

Department of Mathematics and Computer Sciences, Tokushima University, Tokushima 770, Japan

(Received January 7, 1993; Accepted February 3, 1993)

Keywords: Sphere Packing, Lattice, Quadratic Form, Algebraic Number Field, Polytope

Abstract. The classical sphere packing problem has been developed with the number theory, the group theory, the coding theory and so on, but even its fundamental parts are unsolved today. We will show the present situation of the packing problem and some relations among the sphere packing, the number theory and the polytope.