On Optimization Problems on the Polyhedral-Spherical Configurations with their Properties

A class of polyhedral-spherical configurations is introduced as a special case of finite point configurations. Theorems on the properties of such configurations are formulated. A connection of polyhedral-spherical configurations with vertex-located sets is established. An optimization problem on polyhedral-spherical configurations is investigated. Extremal properties of functions defined on the sets are explored.