IV.3.2 The Hexahedron
The Hexahedron, which is the Cube, has six square faces, eight vertices, and twelve edges. A Hexahedron is any polyhedron with six faces, but the Cube is a regular Hexahedron with all its faces square, and three squares around each vertex. The cube is the only regular Hexahedron. The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is also a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is dual to the Octahedron. It has cubical or octahedral symmetry. The cube is the only convex polyhedron whose faces are all squares.
Figure IV.5: The Hexahedron, or the Cube, has six square faces, eight vertices, and twelve edges, and its the dual of the Octahedron.
Plato suggested that the Cube corresponds to the element Earth, because of its four-square regularity, but this same property makes it correspond to Water, whose complex time-time structure is , rather than Earth , because the physical world, described by , is made from Water that is the real vacuum super-fluid as we explained in Chapter II. Also, since the dual of the Hexahedron is the Octahedron, that should corresponds with Air, which is the super-gas state that is the vacuum of the psychical world, and that is why these two solids are mutually orthogonal, just like the two arrows of time which are the folds of super-symmetry, as we explained in Chapter II.