I made these using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
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RobertLovesPi.net 
Fantastic! I was sure it is possible to construct rhombic triacontahedron from icosahedra, which has the same symmetry. But rhombic dodecahedron has different symmetry.
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I think you’d need dodecahedra to build a rhombic triacontahedron. https://robertlovespi.net/2015/11/05/92-dodecahedra-arranged-as-a-single-rhombic-triacontahedron/
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Of course yes. I mean, both dodecahedron and icosahedron have icosahedral symmetry whole rhombic dodecahedron has different cubic symmetry. And the possibility to construct a polyhedron of some symmetry from polyhedra of some different symmetry is counter-intuitive. In this case it is possible (!), but HOW did you get the idea of doing so?
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I got the idea from a Zome model of the rhombic dodecahedron, which uses yellow struts, which are triangular, and attach twenty to a node — like the twenty triangles of an icosahedron.
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Hi guys, you can notice in buckminster Fuller work that each vertices of icosahedron cuts each faces of the rhombic dodecahedron with the golden ratio. This is why this two shapes are like a bridge between thé pentagonal golden ratio geometry and the cubic or hexagonal √2 ratio geometry. This is absolutly mind blowing.
Zentou Sony
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