Satellite constellation designers take into consideration the entire telecommunication network and their design choices are influenced by many factors including: number of satellites, orbital characteristics, coverage area, network interconnections, system cost, and complexity. When the satellite constellation design method does not include a large number of possible configurations, then the final result of the design process is a suboptimal solution. Flower Constellation (FC) design provides a relatively new design approach which can overcome this problem. The time evolution of the FC theory is here summarized and the fundamental mathematics allowing the constellation design is provided. In particular, the theory is applied to the design and optimization of constellations maximizing the global coverage and the network connectivity via intersatellite links. Performance results are compared to the classical type of satellite constellations, i.e., the Walker Constellations. The performance improvement provided by FC design with respect to Walker Constellation design is shown. Finally, considerations regarding the cost for deployment and orbital control are also provided.