Is it possible to cut a regular tetrahedron with edge length 100 into regular tetrahedrons with edges of length less than 1 and regular octahedrons with edges of length less than 1?


1 Answer 1


Yes. There's a solid tiling of tetrahedra and octahedra that fills a tetraderon. Making a sufficiently large tetrahedron this way and scaling is down to the right size solves the problem.

enter image description here

One way to obtain the tiling is to cut to tetradhedron with slices parallel to each face that are spaced apart at even intervals of $1/200^{th}$ of its height.

  • $\begingroup$ Perfect answer to nice question and +1 for the picture. (But shouldn't the picture end at a point at the bottom, rather than an edge?) $\endgroup$
    – BmyGuest
    Jul 23, 2015 at 7:57
  • $\begingroup$ @BmyGuest Yes, I couldn't find a picture that had the tiling in the shape of a tetrahedron, this was the closest I saw. $\endgroup$
    – xnor
    Jul 23, 2015 at 8:00
  • 2
    $\begingroup$ Here's a very bad photoshop I made using the above image showing it as a tetrahedron i.stack.imgur.com/CETMj.png $\endgroup$ Jul 23, 2015 at 13:01

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