A line broken by an inner negative space rotates to form an unknot, a continuous line with no overlapping. The component, as well as the resulting structure, can be unraveled to form a loop. The unknot at home in the studio:
tri unknot
tri unicursal knot
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. It’s a simple knot that makes a single …
knot theories II
the development of partial-dimensional geometry 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 …
layered multi polygon knot
A group of three similar polygons rotate to form a knot. Multiple glass layers show colors, the knot itself, and a faint outline.
metatronic solid (hexahedron)
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 …
unicursal hex knot
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 …
tri angle polygonal knot
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 …
lattice tile
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 …
knot tiling triangle-faced polyhedra
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 …
exploded hexahedron tiled with a plane-filling curve
A single line bisects a hollow cube into two mirrored sections, revealing a second, smaller solid cube inside which supports the three pieces when suspended from the top corner. The bisecting line (curve) is plane-filling, and each face of the exploded hexahedron is identical. Put another way, when the 2 black pieces are fit together …
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