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 (that can be seen in the photo) 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 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)
