Ignoring rotations, there are exactly thirty ways to arrange six unique images on a cube. Each of the thirty cubes in this piece is tiled with a unique arrangement from a set of six tiles composed of curves and lines.
These tiles work with Truchet tiling in that they contain similar elements (different numbers of noodles and nubs) in different configurations. This becomes more obvious when there is no space between the tiles.
These tiles themselves can cover the plane in any random arrangement. We’ll come back to the idea of filling a large, flat space with these tiles, but for right now, we’re only concerned with putting one tile on each face of a cube, considering tile rotations as equivalent to one another and making sure each cube has a unique arrangement of those tiles.
The table J.H. Conway created for his solution to MacMahon’s problem helped immensely with keeping all this straight while I was working on it.
My version of his table diagram assumes that one side of the cube has already been stamped with the “plus.” After cutting the cubes out of walnut, I placed the cubes on a large printout of the diagram as I stamped them with the different tiles.
The base for the cubes to rest on uses a randomly chosen arrangement of connected / outlined tiles etched on the surface of a circular mirror.
The cubes can be arranged so that patterns emerge across perpendicular planes regardless of their placement.
The piece is made up of a 12″ circular base and thirty 1.75″ cubes, so the dimensions are variable depending on the arrangement of the cubes.
This piece was part of the Knoxville Arts Alliance Show No Bigger Than a Breadbox in 2025 and will be on display as a part of the 2025 Dogwood Regional Exhibition in July.