knot theories II

  • tri unknot

    tri unknot

    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 unicursal knot

    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 […]

  • layered multi polygon knot

    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)

    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

    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

    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

    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

    knot tiling triangle-faced polyhedra

    A single shape tiles the faces of all three equilateral triangle-faced regular polyhedra with knots.

  • tile hexahedron

    tile 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. It’s always a little hard to tell what you’re looking at with sculptures, so this video shows multiple angles:

  • scale tile listing band

    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. 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 […]