exploded hexahedron tiled with a plane-filling curve



A single line bisects a hollow cube into two mirrored sections, revealing a second, smaller solid cube inside which supports the three pieces when suspended from the top corner. The bisecting line (curve) is plane-filling, and each face of the exploded hexahedron is identical.

Put another way, when the 2 black pieces are fit together to form a cube, the line that divides the cube (and so, each face of the cube) is an example of a space-filling curve, adjusted slightly for use as a face solid.

The diagram here shows the first 4 iterations of this curve although only the first one is used in this piece. It may look like the Hilbert curve at first, but while it’s ok for a space-filling curve to start at the left and end at the right, to use a curve to tile the faces of a polyhedron, it will have to follow a more circuitous path.