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You can inscribe another tetrahedron in the cube

 

The yellow tetrahedron joins the vertices left free by the red one.

Leave out the cube, and you have a shape discovered by the astronomer Kepler, whose research into planetary orbits was used by Newton. He called this a Stella Octangula.

More mathematical images (start of page)

More mathematical images (Kepler's stella octangula)

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