I made these using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

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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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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