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Decomposition of the Truncated Octahedron into Parallelepipeds

This is a problem I found in the Open Problem Garden of Matt DeVos and Robert Samal. The question is, whether one can decompose a truncated octahedron into parallelepipeds.

The decomposition may be obtained in two steps:

One such decomposition is shown in the above javaview picture. There is also an 3D-applet version of the above picture. It was created using a var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E"));