Icosahedron in Cube

Twelve vertices of an icosahedron are naturally split into 3 groups of four so that, in each group, pairs of vertices are joined by parallel edges. So there are three groups of parallel edges, edges from different groups being perpendicular. As such, these edges fit into opposite faces of a cube. In the applet below pairs of opposite edges joined to form a rectangle. There are three of them along each of the three basic planes.

And here is an entire icosahedron embedded in a cube.

Drag the mouse to rotate the dodecahedron. Use the right button to remove and put back individual faces.

(Acknowledgement: I have learned most of Java details from the implementation by Meiko Rachimow.)

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Copyright © 1996-2012 Alexander Bogomolny