multi-dimensional hex knots

Two sets of interlocked hexagonal rings traverse three color fields.

The flat painting and the sculptural painting are versions of the same knot using 2d and 3d grids. However, the 3d knot is not a projection of the 2d knot on a solid object. It’s more like the 3d knot is wrapped with a version of the knot that conforms to a grid on its surface.

paper version always comes first

I did two small versions of the 2d knot. The more black and white one is spray paint; the one with more colors is acrylic paint and pencil.

I have used a for similar to this one as a base to hold up a few other smaller sculptures. It’s great because it can hold a cube, sits flat on a surface, and is easy to construct. This one was much larger than previous ones.

This is what I used as a guide. Measuring would have been a recipe for disaster. Draping the guide over the piece let me have some actual wiggle room.
I always feel bad for my templates. So much work goes in to them and they just get recycled. I try to make it up to them by taking one last portrait before they hit the bin.
2d in progress
3d in progress
walkaround of the finished sculptural painting

Limited edition serigraph prints of this design are available.

A small version of the 2d painting was on display in the City County Building in Knoxville in 2023.

multi-dimensional hex knots (flat); paint on wood; 33″ square
multi-dimensional hex knots (sculpture); paint on wood; 24″ x 24″ x 24″

relationship to aperiodic monotiles

As if there weren’t enough ideas in this piece, here’s one more: the colored shapes behind the knot, either on the flat painting or as seen isometrically on the sculptural one, are part of the progression of the aperiodic monotile transformations. In other words, even though the arrangement of the red, green, and blue shapes can be arranged to form a hexagon as they are here, they can also be arranged to aperiodically tile a plane.

“Oh, cool.”

Craig Kaplan

(I was lucky enough to share this piece and its explanation with Craig Kaplan in person, but he is welcome to correct or retract his statement which was part of our discussion.)

(artwork medium)