Platonic solids is the therm well known for a set of 5 regular polyhedras, which are known since ancient Greek period. They have some interesting properties such as duality between pairs of them, and they belong in to the basic knowledge of space division. Regular polyhedra is made only from one type of polygon, and this works just for triangle, square and pentagon, for the other, it is impossible in 3D space. There are other interesting supplements for this topic in 4D.
In my case first I studied their properties, than I decided which I´m going to use for my purpose. I chose dodecahedron and icosahedron, one inside the other, because of their volume closest to the volume of sphere at given diameter, because of their significant play of thickness between their surfaces. I used them as turncated at exact level to be hollow like a bowl or vase.
Platonic solids brochure PDF.