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 reserved for the 2-dimensional version of this knot.

This piece shows that a single triangular tile can tile a flat plane as well as the Platonic deltahedra.

Exhibition history for this piece

  • Schwarzbart Gallery, January 2022
  • Joint Mathematics Meeting (Boston), January 2023
  • Emporium Center, April 2023 (No Bigger Than a Breadbox show)