Knowledge of polyhedra has been used since ancient times by the civilizations of Egypt, Mesopotamia, and Africa. Ancient people believed in the superpower of perfect structures and symmetric bodies. Pythagoras of Samos (c. 582–507 BC) created a cosmological doctrine that linked regular polyhedra with the structure of the universe. The Pythagoreans believed that the elements of primitive beings had the form of regular polyhedra, namely: fire—a tetrahedron, earth—a hexahedron, air—an octahedron, and water—an icosahedron. This chapter offers many problems related to the simplest convex polyhedra—prisms and pyramids, as well as problems related to regular and semi-regular polyhedra. The reader will learn how an unfolding of a polyhedron and looking at its unfolded analogue on a plane, helps to find relationships between angles or distances in a three-dimensional figure. Some natural or synthesized molecules or crystals in the form of regular or semi-regular polyhedra are discussed with explanations of their structure based on Euler’s formula, chemistry and theorems of stereometry.