Cube Trisection, Cake Sharing, Non-Congruent Pieces

thingiverse

Make a bunch of cubes, flip them around, connect them, and have fun! The present design is based on the well-known "cake-sharing" problem. If you have a square cake with icing all around, how can you cut it in a way such that three people each get the same amount, including icing? The essential idea is to take advantage of the center of the square and think of the square edges as the bases of some triangles, which all have the same altitude. We can slice a cube in a similar way and obtain three pieces with the same volume. There are certainly many ways to do that. In this design, I added some jigsaw connectors so that one can slide them into each other for a cube or, if so desired, other shapes. Please note that, in spite of the connectors, the three pieces still have the same volume! Two versions of shelled pieces are included in case one wants some boxes. A plain version, without connectors, is also included. The cube is 50mm x 50mm x 50mm. Of course, a cube can be trisected into three congruent pieces in many different ways (see my other designs). Have fun!