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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:

- We observe that the truncated octahedron is a zonotope and thus may be constructed as on David Eppstein's geometry junkyard.
- Zonotopes come with a natural decomposition into parallelepipeds. The edges of the parallelepipeds are parallel to the vectors used to construct the zonotope.