A shape with interlocking edges tiles a plane.
The edges of these planes bend to form a hexahedron.
A cube or rectangular solid of any size can be created from any multiple of this component. This one uses 24 components and makes a cube.
Tag: metal
tile hexahedron
single component four components / single side of hexahedron first three sides together components becoming the cube 
scale tile listing band
Twenty-three identical scales are tied together in a continuous loop representing a non-orientable surface. A pattern of accented hexagons covers interlocking segments which twist and bend in an infinite knot.
multiple component illustration 
single component illustration, hexagons highlighted This band is smaller than others I have done so far, so it is self-supporting and can be displayed resting on a surface or suspended from above.
The component illustration highlights the hexagonal counter-spaces which were painted gold.
The final piece is approximately 18″ in diameter, but let me know if there is a better way to notate the dimensions of something like this….
up close with some other cool art in the background 
direct view 
infinity perspective 
paper maquette This piece was accepted as a part of the 2022 Bridges Conference in Aalto, Finland.
It is now part of the permanent collection of the Experience Workshop’s traveling collection.
tercet knot progression with self-similar encompassment
Self-similarity within structures is always fascinating to me. After creating a knot encompassed in an element of itself (above), I thought it would be nice to also show a progression from the simplest component to a much more complex version of itself which would in turn cycle back to the beginning.
this illustrates the progression seen on the individual pieces Each of the final pieces changes slightly from the one before it to create the cycle.
notes and to do list in sketchbook You may be wondering, where did that nice oxidization come from? In my studio, I have a clearly labeled bottle of RUST JUICE for just such an occasion. On properly pickled metal, you can actually see the rust form within seconds.
my metal prep schedule and checklist. mostly because I quickly forget how many times I’ve sprayed something. 
the first version was done on galvanized steel, which oxidizes in a different way 
axonometric scale listing band
the question
Is there a shape, which when repeated, can create a Mobius strip?
Yep, there is. Really all you have to do is chop up a strip into squares, however many pieces you want and there you go, done.
That was easy. Maybe I’m not asking the right question.
the better question
Is there an asymmetrical shape which interlocks with itself to create a continuous band on a non-orientable surface?
That one is a lot better, but it seems a little unrealistic that I would have started out wondering that instead of the first question.
an answer
To create a simple shape that tiles rectilinearly, you can start with a square, and any change you make to one side, you make the opposite change to the other side. So, if you squish in from the right, you squish out from the left. Continue until you have something interesting.
Listing bands have the additional twist (pun intended) that at some point, the top of one tile (or “scale” which is what I’m calling the individual components) is eventually going to have to fit in with the reverse of the bottom of another. Only bands made up of odd numbers of scales will work. This is probably easiest to understand if you consider that just one scale, twisted into a band would have to fit into itself this way, and one is an odd number. Even numbers simply twist too many times for an asymmetrical scale.
This particular band is made up of nineteen individual scales. They were fabricated from .03″ mild steel and allowed to rust naturally. The scales were designed so that just the right amount of twist and bend could happen with this size and material.
one finished scale and its idealized shape 
notes and sketches 
wire used to links scales together The base was constructed from fir and walnut. Displaying a band this large was a challenge, since it sort of collapses if it’s set on the floor. The base allows easy viewing from multiple angles, which is really necessary to get an idea of how complex the shape is. Fortunately there’s a sweet spot that allows just the right distribution of weight so that it’s balanced and sturdy on the base.
In lieu of a maquette, I did a bunch of calculations, which is usually a recipe for disappointment. Luck was on my side this time.
