Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

where can I find a proof that truncated octahedron tiles Euclidean 3D space?

share|cite|improve this question
2  
You mean references for the bitruncated cubic honeycomb? Sadly, there doesn't seem to be an online version of Grünbaum's paper... – J. M. Dec 4 '10 at 0:02

To tile space, center them at lattice points and at the centers of lattice cubes (i.e. lattice points plus $(\frac{1}{2}, \frac{1}{2}, \frac{1}{2})$). The eight faces of the octahedron face the neighboring 8 vertices of the "other" lattice (the one relatively shifted by $(\frac{1}{2}, \frac{1}{2}, \frac{1}{2})$), while the six truncated corners face the six neighbor vertices on the "same" lattice.

Most sources (often crystallographic) consider this to be obvious enough that it needs no proof.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.