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The 12 points of the stellated dodecahedron form an invisible icosahedron. (We also have a model where the icosahedron is added as well). These are the two 5 symmetry platonic solids.
The 5 symmetry of these shapes is what creates the instability that allows life to exist so it is natural that the DNA should be based on them.
The five symmetry also means that all the line lengths are in golden mean proportions. In fact this is the primary geometric expression of the Golden Ratio. No wonder it is such a pleasing and entrancing form !