Knot Structured

George W. Hart

This is a 7-inch diameter one-of-a-kind sculpture assembled from thirty identical pieces of laser-cut wood (aspen). Although it is titled Knot Structured, it is, of course, highly structured. Each piece is a kind of bent H-shaped form, with a central hole and four arms. The aspen is quite light in color but the laser-cut edges are a rich contrasting brown. There are twenty openings in the shape of a trefoil knot and twelve openings in the shape of a "pentafoil" knot. Each trefoil knot is linked to three neighboring pentafoil knots, and each pentafoil knot is linked to five neighboring trefoil knots. In addition, there are sixty unknotted holes.

The individual pieces of wood are flat (planar) and just barely pass by each other as they link over and under. Three flat C-shaped curves make up each trefoil and five flat S-shaped curves make up each pentafoil. The structure as a whole has icosahedral symmetry, so the same structure is found on all sides. Here is an image from the other side:

Geometrically, the thirty parts lie in the face planes of a rhombic triacontahedron and the sculpture as a whole can be understood as a subset of "the first stellation of the rhombic triacontahedron". Assembling and gluing the parts was something of a tricky puzzle.

Addendum, 2016

I created this in 2003 and sent it to Martin Gardner, but I don't know what happened to it since nor where it is now.
Recently I remade it, somewhat larger, using cable ties so it is easier for others to replicate. Here's the newer version.

Copyright 2003, George W. Hart