The polycube constructions floating in the headspace of the silhouettes fit together to form the cube at the top of the painting. The orientation of the polycubes is the same in both locations. In another orientation, each polycube casts a shadow the same shape as the tiles behind. The cube casts its own hexagonal shadow in the same way.

In the context of the theme of Art of Community, the three individuals (literally) have a piece to the puzzle, and each thinks his idea could cover everything. Yet, not every orientation of the polycubes will tile the plane.

Here’s what they might be thinking about: if a cube is broken evenly into three polycubes that fit together to reconstruct the parent cube, does each polycube always have at least one orientation which casts a plane-tiling shadow?

This piece will soon be on view at the University of Tennessee Hospital as part of its Art of Community show.