relativity requires an observer and observed- at least two positions in space.
More than one position in space disproves singularity.
"Unity is plural and at a minimum two"...Bucky Fuller
The minimal 3D defined space is a tetra{4}hedron. We can conceptually sub-divided the tetrahedron eternally ergo multiplication-by-division LINK of a finite whole, and, in so doing, we still can never ever have less than the 26 characteristics that define a tetra{4}hedron.
12 surface angles,
6 edges,
4 openings
4 vertexes
ergo 3D volume of ever decreasing size and physicall speaking any such subdivision ultra-micro occupied space, is limited by the amount of energy one can accumulate --from a finite Universe-- and directly go the next level of sub-division { quantization }.
Any talk of infinite sub-division ---Bucky Fuller himself speculated--- inherently incurs an eternal process of doing so. I dont think Universe does that.
The area of the spherical cubo{6}-oct{8}ahedrons four equatorial bisections, is equal to the surface area of that spherical cubo{6}-octa{8}hedron. Archimedes was first to discover this fact and in some ways reflects what we know about black holes, i.e. what is inside a black hole is expressed on its event horizon surface.
There is an eternally existent finite set of Metaphysical1, cosmic principles, that, complement the eternally existent set of possible occupied space manifestations.
There can never ever exist more than the finite set of five, regular/symmetrical, and convex polyhedra. Better chance that toyotas that breed purple magic Unicorns, tho my guess is that is also and impossible occupied Space occurrence.