Explore the fascinating world of Platonic solids in this 26-minute video lecture from the Universal Hyperbolic Geometry series. Delve into the fundamental symmetry and historical significance of these regular solids, including the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. Discover their importance to ancient Greek mathematicians, particularly Euclid's treatment in Book 13 of The Elements. Learn about the symmetry properties, polyhedra classification, and Euclid's derived formulas. Examine Euler's fundamental relation for polyhedra and consider a unique perspective of Platonic solids as regular tilings of a sphere. Gain insights into these remarkable geometric objects that have captivated mathematicians for millennia and their potential applications in hyperbolic settings.