In the mean time i deepened the geometry of the implosive sphere.
On the net You can find some schematics that show the interior of the implosive device, referring to the Trinity's gadget or to the bomb of Nagasaki.
But in my opinion the platonic solid that were used was not correct. It seems that it was used a truncated icosahedron, but the photo below depicts a different solid, i tought at the dodecahedron.
I tried to reproduce the shape of the sphere and it seems to me that i was right. Here You can compare the actual photo of a test unit with my simulation.
Using this solid we have only two types of HE charges: a regular and an irregular pentagon.