Images for Mathematics

Twenty parallelepipeds to create a triacontahedron

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The rhombic triacontahedron can be coloured with five colours so that, around the vertices where 5 faces arrive, these faces have different colours (as in the photo). 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 using these 20 parallelepipeds, by disposing the parallelepiped so that attached faces will have the same colour. You can see also a net.

The image belongs to the sections...:
The symmetry group of the dodecahedron (*532) (Symmetry)
The rhombic triacontahedron puzzle (3D geometry)


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