The 1D quantum vacuum can be partitioned into infinitely many subintervals. The norm of this partition is equal to the length of the largest subinterval and is denoted by ||P||. However, if these subintervals are of equal length then ||P|| represents the irreducible unit of the quantum vacuum. For all practical purposes, the norm is equivalent to the Planck length.
The 2D quantum vacuum is then the development of unit squares with sides as given by the norm vacuum. The 3D quantum vacuum is then the development of cubic norm vacuum extending infinitely in every possible directions of space-time. Moreover, with every 3D tessellation of unit cubic norm vacuum can be found a volume minimizing compactification of a tetrahedral tessellation of side √2 of the unit norm vacuum. The cubic norm vacuum can represent the quantum vacuum space-time structure of some leptons while the tetrahedral norm vacuum can represent space-time structure of some quark’s flavors. The three others non-tessellatable Platonic solids would be the octahedron, icosahedron, and the dodecahedron.


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