# Twenty parallelepipeds to create a triacontahedron

How to make a puzzle. The rhombic triacontahedron can be coloured with 5 colours so that, around each vertex 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 5 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. The figure shows the nets of 4 parallelepipeds.

© matematita

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The rhombic triacontahedron puzzle (3D geometry)