The problem of packing congruent copies of an object in space as densely as possible is our topic this month. Spheres can be packed with a density of approximately 74.05% (a computer proof of this fact was given by Thomas Hales in 1998). Very recently (see here), it has been shown that regular tetrahedra can be packed with a density of approximately 85.63% (although this has not yet been shown to be optimal).
This month's problem is to find the densest packing of regular octahedra that you can.