Cube
included into octahedron
(The image is an applet: you can click and drag it).
The vertices of the cube lie on the edges of the octahedron. The cube vertices split the octahedron edges in two parts whose ratio is sqrt(2).
Note: Cube is the dual of Octahedron, therefore the octahedron centers are the vertices of an included cube. This is just another way to inscribe a cube into an octahedron.
The applet shows the previous inclusion only. (I had to choose and the selected inclusion looks more "beautiful" :-)
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