Explore the symmetries and canonical structures within the cube and octahedron in this 24-minute video on Universal Hyperbolic Geometry. Delve into the 2-fold, 3-fold, and 4-fold symmetries generated in the cube, while examining bipartite graphs and their relationship to these Platonic solids. Gain deeper insights into the rigid motions of the cube, with a focus on the crucial concept of even and odd symmetries. Learn about graph theory terminology, flat photonic solids, face diameters, and vertex diagonals as you uncover the fascinating world of geometric structures and their properties.