
Originally Posted by
AntonioLao
There exist Rubik’s cubes that are 2x2x2, 3x3x3, 4x4x4, 5x5x5, and so on, theoretically, ad infinitum. All these cubes, regardless of their dimensional orders, shared something in common: six faces (F), 8 corners or vertices (V), and 12 edges (E). Furthermore, their numbers are related by Euler’s formula for all convex polyhedrons without holes, F + V – E = 2. These six faces could then be labeled as right (R), left (L), front (F), back (B), top (T), and bottom or down (D). Three of these could combine to form 8 directional properties: RTF, RTB, RDF, RDB, LTF, LTB, LDF, and LDB. These properties are more important than the actual counting of faces, vertices, and edges, and hence applicable to all polyhedrons or any 3D object that are not temporally dependent.
Although, mathematically speaking, a particular Möbius strip has only one face and one edge, requiring it to have only 2 vertices satisfying Euler’s formula, nevertheless, it has all the 8 directional properties as long as a given longitudinal temporal direction is attached to these two vertices. Therefore, each Rubik’s cube is topologically equivalent to two linked Möbius strips having unique time direction. This formed a unit for all space-time points. It could then be described by using Hadamard matrices as discussed elsewhere.