Twenty parallelepipeds to create a triacontahedron
The rhombic triacontahedron can be coloured with five colours so that, around the vertices where 5 faces arrive, these faces have different colours. There are two different ways to make a parallelepiped that has six faces equal to the rhombi that are faces of the triacontahedron and 10 ways to choose 3 colours among the 6 given colours. We can rebuild the rhombic triacontahedron (as we can see in the photo) using these 20 parallelepipeds, by disposing the parallelepiped so that attached faces will have the same colour. You can see also a net.
© matematita
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The rhombic triacontahedron puzzle (3D geometry)
