thirty unique Truchet-tiled cubes

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.

I named the tiles nubs, frown, tav, shrug, noodles, and plus. Notice that all the shapes are actually some combination of noodles and / or nubs.
The way the tiles connect becomes more obvious when there is no space in between.
a simple arrangement showing variations and connections

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.
cubes after being stamped with the tiles and polished with oil for inevitable handling
The cubes can be arranged so that patterns emerge across perpendicular planes regardless of their placement. Any arrangement works for creating a stack with a tiled exterior.
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.
February 2025
No Bigger Than a Breadbox
Knoxville Arts Alliance
Spring 2025
2025 Dogwood Regional Exhibition
Red Gallery, Knoxville, TN
January 2026
Joint Mathematics Meetings
Washington, D.C.

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