I describe a three-dimensional puzzle which I have devised, originally conceived as a variation on the Giant Pyramid puzzle by Gordon Bros. It consists of seven pieces, each made up of five cuboctahedra, which can be fitted together into a regular tetrahedron with five cuboctahedra on each edge.
Photographs by Maria Fremlin
The three yellow pieces are identical and are coded in the files coltwist.scad and coltwist.stl; similarly, the blue pieces (which are mirror images of the yellow pieces) are coded in cortwist.scad and cortwist.stl, while the red piece is in cocross.scad and cocross.stl.
For a description of the SCAD language and free software for creating stl files from scad programs, see the OpenSCAD site.
The pieces here were built with a Makerbot Replicator 2X. You will see that there are holes in some of the faces, due to a weakness in the Makerware program which I have not yet figured out a patch for.
With one blue piece and one yellow piece, you can make a tetrahedron with three cuboctahedra on each edge; with two blue pieces and two yellow pieces, you can make a tetrahedron with four cuboctahedra on each edge. These are both classics, though normally realized with spheres rather than cuboctahedra.