This collection of artworks further explores the use of repeated, simple shapes and lines translated or rotated to create complexity in a knot design. Each piece is based on a component, shown on the respective artwork posts.
A variety of techniques and media were used to bring the designs to life. The shapes and symbols they create are purely geometry, with no hidden meaning beyond the beauty of intricacy.
All work in this collection was created for and displayed at the Schwarzbart Gallery during January of 2022.
A line broken by an inner negative space rotates to form an unknot, a continuous line with no overlapping. The component used as the basis for this piece, as well as the resulting structure, can be unraveled to form a loop.
Tri Unknot was on display at the McGhee Tyson Airport (TYS) in 2023.
A unicursal line is inlaid in copper on the face of a hollow truncated tetrahedron. The knot creates a cognitive visual illusion of three shapes versus two.
The illusion that there are sort of 3 shapes but only really 1 is something I like about this one.
A group of three similar polygons rotate to form a knot. Multiple glass layers show colors, the knot itself, and a faint outline.
As a test, I made a small version with some glass squares I had left over from another test piece. The goal was to create different layers for each of the colors, the black line, and a frosted outline of the whole thing.
As a test, I made a small version with some glass squares I had left over from another test piece. The goal was to create different layers for each of the colors, the black line, and a frosted outline of the whole thing.
The repeated component in this piece had specific colors with it. The idea was to have overlapping layers of transparency in the color. Part of this piece was experimenting with knot lines on an axonometric grid.
The maquette was made with inkjet printing on acetate. It doesn’t look terrible, but I wanted the whole piece to be much larger. This was more for concept than anything, just to see if it might look cool. And it does! But it’s just a stack of loose glass.
The final piece has a frame, I used paint for the colors, vinyl for the black, and etched the glass for the…etched glass part. It ended up being the white background plus 3 layers of glass which fit in slots in the frame.
Four lines make a reversed knot pattern covering all faces of a hexahedron, regardless of rotation (this same pattern can tile a plane).
One of my most basic rules for knot creation is that knot lines only cross one another in pairs. Any more than two lines appearing to overlap in the same place doesn’t allow for clearly implying that one line is over another. And it’s confusing.
In this design, a diagonal line cuts a square in half. Three more lines attempt to converge in the center of the square. A ripple radiates from this center point, forcing these subsequent lines to bend around the point they would all intersect. The positioning of the lines allows a cube to be formed.
This is the second (or maybe third) in a series of hollow polyhedra based on this concept, taking its name from Metatron, a figure associated with the geometry of regular polyhedra.
After cutting the lines and carefully (read: dangerously) beveling the edges, I glued the faces together.
It looks great when light is shining through it, but displaying it resting on one of the faces seems like a waste.
The stand obscures much less of the finished piece and presents a much more interesting viewing angle.
This piece was a part of the The Arts & Culture Alliance’s 16th annual National Juried Exhibition and displayed at the Emporium in 2022.
A self-intersecting line rotates to create a hexagonal shape. The line can be followed from any point all the way around to loop back to its beginning.
This was another experiment involving cut paper on charred wood. My first attempt at realizing this design was with wire in encaustic medium, shown here.
Even though it was tedious, things were going great until I sealed the next layer. The heat required to fuse the wax (which isn’t much) was enough to bend the very thin brass wire out of whack. After that, I just threw in another experiment, using crumpled tissue paper as a layer in the encaustic.
It was interesting, but I wanted something a little neater. And less disaster-prone. So, I went with cut paper. On charred wood. What could go wrong with knives and fire?
A parallelogram and a triangular line rotate to create an overall triangular shape. Encaustic medium covers gilded ink.
My first step was putting the main design down in ink. (I phrased the media used in this piece as “Patty Ink” because it once belonged to Pat Lauderdale, someone who always encouraged my artistic endeavors. She died in 2016 and I was given some of her art supplies, so I like to make reference whenever I use them.)
Next, I put gold leaf along the lines, scraping off some of the leaf to reveal the color underneath.
Finally, I added a few layers of encaustic wax to give it a little more depth. The frame is charred wood.
This piece was on display in the Schwarzbart Gallery in 2022.
One component of an interlocking tile extends its connectors and uses color variations to imply depth and an isometric perspective. Stained veneer is inlaid in a wood background.
This piece involves a bit of experimentation with an isometric knot. The interlocking square shapes require more than one color to give the effect that they are 3d-ish.
This piece is a single tile with its connectors extended. A repetition of the tile looks more like this:
Keeping track of the colors in just one tile was involved enough for me:
This piece was on display in the Schwarzbart Gallery and at the City-County Building in Knoxville in 2022.
A single shape tiles the faces of all three equilateral triangle-faced regular polyhedra with knots. Only the bend angle of the shape changes between the solids. The knot also tiles the plane.
Notice that the knot on the tetrahedron appears to be interlocked triangles; squares for the octahedron; and pentagons for the dodecahedron. Hexagons are reserved for the 2-dimensional version of this knot.
This piece shows that a single triangular tile can tile a flat plane as well as the Platonic deltahedra.
Exhibition history for this piece
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.
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.
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….
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.