More concentric icosidodecahedra
A regular icosahedron inside an icosidodecahedron, inside a rhombicosidodecahedron, inside a rhombitruncated icosidodecahedron:
Four nested polyhedra
1230 pieces: 314 balls, 701 rods, 40 pentagons, 115 squares, 60 rhombuses (6.41 kg)
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Only the two outer bodies, namely the rhombitruncated icosidodecahedron and the rhombicosidodecahedron, are truly concentric however. Their bases are respectively labelled idrt and rid in the following, left-hand picture; as can be seen, the latter rests over a half icosidodecahedron, so that their centerpoints exactly match, as we did in Concentric icosidodecahedra. But the icosidodecahedron (labelled id) is raised from an inner pentagonal face of the rhombicosidodecahedron on a pentagonal antiprism, which positions its centerpoint about 6 mm too high. And the icosahedron (already built in the picture, unlabelled) is raised from the icosidodecahedron on a pentagonal pyramid, which again positions its centerpoint about 4 mm too high relative to the icosidodecahedron, for a total of about 10 mm.
The following pictures show six steps of the construction. In the fourth one, the vertical green rod through the hole in the pentagonal panel is attached to the top vertex of the inner icosahedron; the fifth picture shows how this rod can be fixed with a ball, although it does not fully pass through the pentagonal panel closing the rhombicosidodecahedron. This contributes to stabilizing the icosahedron.
Four nested polyhedra, step 1
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Four nested polyhedra, step 2
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Four nested polyhedra, step 3
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Four nested polyhedra, step 4
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Four nested polyhedra, step 5
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Four nested polyhedra, step 6
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We have made a base by attaching a decagonal antiprism to the lower decagonal face of the object. This antiprism becomes deformed by a reinforcement structure placed inside the lower half icosidodecahedron. The structure used is shown in the left-hand picture; the right-hand picture shows an alternative one:
Four nested polyhedra, reinforced base version 1
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Four nested polyhedra, reinforced base version 2
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