Cube 5-Compound and Small Rhombicosidodecahedron
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If you move all the faces of a compound of 5 cubes radially, then at a certain distance the vertices of the 30 squares meet and coincide with the square faces of a small rhombicosidodecahedron. You can also adjust the size to see how the squares relate to the faces of the rhombic triacontahedron.
Contributed by: Sándor Kabai (April 2018)
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"Cube 5-Compound and Small Rhombicosidodecahedron
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http://demonstrations.wolfram.com/Cube5CompoundAndSmallRhombicosidodecahedron/
Wolfram Demonstrations Project
Published: April 20 2018