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 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.

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