Dual solids progression

I have recently stumbled upon a neat little animation of nested dodecahedra and icosahedra. However, something was clearly wrong with it: the duals were not properly aligned - that is, they were not actually touching each other. The lack of mathematical perfection annoyed me so much that I just had to create my own version! Turns out that for the duals to align perfectly, the ratio between two consecutive dodecahedra or icosahedra has to be (5 + 2 Sqrt(5)) / 15.