The paper outlines a program to prove the Kepler conjecture, which states that no sphere packing in three dimensions has a density greater than that of the face-centered cubic lattice packing. The author describes the first step of this program, which involves decomposing space into Delaunay simplices and grouping them into finite configurations called Delaunay stars. A score, related to the density of packings, is assigned to each Delaunay star. The conjecture is 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, the paper shows that every Delaunay star satisfying a certain regularity condition satisfies the conjecture. The main theorem of the paper states that if a Delaunay star is composed entirely of quasi-regular tetrahedra, then its score is less than \(8\,pt\). The proof involves classifying all possible triangulations of the unit sphere and showing that only one triangulation satisfies the required properties. The paper also discusses the compatibility of Delaunay simplices and quasi-regular solids, and provides detailed definitions and lemmas to support the main arguments.The paper outlines a program to prove the Kepler conjecture, which states that no sphere packing in three dimensions has a density greater than that of the face-centered cubic lattice packing. The author describes the first step of this program, which involves decomposing space into Delaunay simplices and grouping them into finite configurations called Delaunay stars. A score, related to the density of packings, is assigned to each Delaunay star. The conjecture is 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, the paper shows that every Delaunay star satisfying a certain regularity condition satisfies the conjecture. The main theorem of the paper states that if a Delaunay star is composed entirely of quasi-regular tetrahedra, then its score is less than \(8\,pt\). The proof involves classifying all possible triangulations of the unit sphere and showing that only one triangulation satisfies the required properties. The paper also discusses the compatibility of Delaunay simplices and quasi-regular solids, and provides detailed definitions and lemmas to support the main arguments.