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This part consists of all five Platonic Solids nested one inside another.
From largest to smallest, there is an icosahedron (20 triangular faces), a dodecahedron (12 pentagonal faces), a hexahedron (6 square faces), a tetrahedron (4 triangular faces) and an octahedron (8 triangular faces).
The overall shape is a Rhombic Triacontrahedron, a combination of an icosahedron and dodecahedron). These can be nested infinitely following the same order.