What if the octagonal (double tetra-hedral) object becomes Fractal? It would tend towards the shape of a _coronavirus_ . The other consideration from my point of view which is different, starting from a simple _point_ the next iteration could be a circle; the next iteration could be a sphere; the next iteration could be a toroid, etc. (a mathematician might be able to put that thought into proper perspective).Yeah it could be double tetrahedron equals octagon from our 3D point of view as in our normal 4-dim spacetime plus another 4-dim Kaluza-Klein-like space and for the 4D hexagon given that Ark clarified the 4D is space-like, you could have Ark's 6-dim conformal geometry which does create complex domains. Given the " Tetrahedron in 3D is what in 4D?", the space-like part might be 5-dim which would fit with for n=4:
Klein geometry - Wikipedia
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You would have a 4-dim conformal metric with an O ( 5, 1 ) conformal structure group.
Simplex - Wikipedia
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FWIW.