We can inscribe a cube in dodecahedron (see this), where $12$ faces of dodecahedron give the $12$ edges of the cube.
Can we inscribe cube in icosahedron?
2026-03-25 06:01:58.1774418518
Icosahedron and inscribed cube
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Dodecahedron and icosahedron are dual to one another. So there would be a way where each vertex of the icosahedron corresponds to an edge of the cube. So you'd have corners of the cube in the centers of some of the faces.
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