Monday, March 08, 2010

Symmetry / Simetria (7)

Icosidodecahedron puzzle
In each of these photos one can see one of the (millions?) of natural solutions of the icosidodecahedron puzzle. In each of these photos we interchange the bottom with the top. This solution is symmetric by a reflection or a central symmetry (here colours do not matter, only numbers matter). This is a symmetry of this solution. This symmetry belongs to the group of this solution. If you exchange (an even permutation) of the numbers you obtain the same natural solution that belongs also to its group. It is the icosahedron's group and it has 120 elements. We just saw a simple way of showing an isomorphism between the icosahedron's group and the group generated by the reflections and the even permutations of {1,2,3,4,5}: {-1,1}xA5.

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