BULL! -- the molecular geometry engine based on Voronoi diagram, quasi-triangulation, and beta-complex. Libraries are available for the power diagram and the ordinary Voronoi diagram of points upon which application programs can be easily built. However, its counterpart for the Voronoi diagram of spheres does not exist despite of enormous applications, particularly those in molecular worlds. In this paper, we present the BULL! library which abbreviates “beta universe library liberandam!” for computing the Voronoi diagram of spheres, transforming it to the quasi-triangulation, and extracting the beta-complex. Being an engine library implemented in the standard C++, application programmers can simply call API-functions of BULL! to build application programs correctly, efficiently, and easily. The BULL! engine is designed so that the application programs developed by embedding API-functions are completely independent of the future modifications of the engine.