  We describe a program to prove the Kepler conjecture on sphere packings. We
then carry out the first step of this program. Each packing determines a
decomposition of space into Delaunay simplices, which are grouped together into
finite configurations called Delaunay stars. A score, which is related to the
density of packings, is assigned to each Delaunay star. We conjecture that the
score of every Delaunay star is at most the score of the stars in the
face-centered cubic and hexagonal close packings. This conjecture implies the
Kepler conjecture. To complete the first step of the program, we show that
every Delaunay star that satisfies a certain regularity condition satisfies the
conjecture.
