# 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 a net of the triacontahedron. You can see also the net of the parallelepipeds: here the first four nets, here the second group of 4, here the third goup, here the fourth group and here the last 4.

© matematita

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The rhombic triacontahedron puzzle (3D geometry)