A single shape shows four negative paths curving around the center where they would otherwise intersect. The resulting arcs weave over and under one another.
Copies of the projected shape can be rotated and aligned to form a hexahedral shell on which the paths combine to form four knots.
This sculpture (metatronic solid) is a hexahedron shell formed from the same face pattern.
This piece was on display at the City County Building in Knoxville, TN in 2024.
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.
The metatronic knot on a solid surface has to be “knocked out,” but is there a way to show the inverse? The not-knot? With an opaque material, not really, but with a translucent medium, not only could you show the knot counter-spaces, but you could view the inside and outside simultaneously.
This piece is best viewed with abundant sharp light such as sunlight.
Sculpture usually has to make a compromise because in anything but zero gravity, it has to rest on something. This means you don’t get to see what’s on the bottom. An artist isn’t likely to put something interesting in a place no one can see. In this case, I wanted to make sure a viewer saw how the knot pattern worked out on all six sides, leaving nothing to doubt.
Something of added interest: the pattern used in metatronic knots works regardless of rotation; any of the faces can be rotated and the knot pattern still works fine.
Although the main challenge of creating the metatronic solids was applying knot patterns to regular polyhedra, each face was interesting itself.
The first iteration of the faces was the hexahedron. I thought would be fun to use the face of a hexahedron, a square, to create a cube, but by stacking copies of the face instead of rotating them along their edges.
For the next version I focused on just one face, a triangle from a tetrahedron. I used gold leaf poles to elevate the shape off of the background.
The radial lines in the knot design were emphasized by darker wood in the background.
The dodecahedron face, a pentagon has many more radial lines. They were inlaid with a contrasting wood.
There’s one more of the square / hexahedron. This one was a little more involved, so there’s a separate post devoted to it.
Three lines make a reversed knot pattern covering all faces of a tetrahedron, regardless of rotation (this same pattern can tile a plane).
The first in a series of polyhedra shells based on this concept, taking its name from Metatron, a figure associated with the geometry of regular polyhedra.
This piece was included in the 21st Master Woodworkers Show in Knoxville, TN.
