Sphere packings. I (Q2365323)

The Kepler conjecture asserts that no packing of equal spheres in 3-space has density exceeding that of the face-centered cubic lattice packing. After several attempts to prove this most famous geometric problem the author has developed a program which combines geometric strategies (e.g. space-decomposition into Delaunay simplices), a reduction strategy to finitely many optimization problems and a computer aided attack to these problems. In this first (of perhaps 4 or 5) papers [for part II see the paper Zbl 0883.52013 below] the author solves some restricted special cases.