How many regular tetrahedrons with edges of length square root of 2 can be packed into a cube with edges of...

geometry/tetrahedra.in.cube New, unsolved

New entry, edited from material collected for the archive and not yet in a released version.

Problem

How many regular tetrahedrons with edges of length square root of 2 can
be packed into a cube with edges of length 2?

Show solution

No solution was found in the collected postings.

Clue: the answer is more than 9.

Another clue: solve the problem for a box of size 2x2x1 first.

-- Philip Gibbs <phil@eurocontrol.fr> (poser of the problem)

Well, this hint makes me think the answer is more than 10 (since my
best answer for 2x2x1 is 5), but I can't see how to get any more.

-- David Wayne Ring <dwr2560@tamuts.tamu.edu>