Five cubes in a dodecahedron

The figure shows how it is possible to choose (in 5 different ways) 8 of the 20 vertices of a dodecahedron so that they are the vertices of a cube. The 5 resulting cubes are obtained from each other by rotation around the symmetry axis of the dodecahedron which passes through the centers of two opposite faces. 

Initially, the figure in the center is the composition of the five cubes. Clicking on one of the cubes removes it from the compound and places it in the margin, on the square of the same color. A second click snaps it back into place. Click & drag anywhere on the figure to change the point of view.

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