Polypolypolyhedron

An orderly mess of 60 woven plastic rods.

Designed and constructed in November, 2009.

[Polypolypolyhedron illuminated from within]

Illuminated from within by a blue LED.

The Polypolypolyhedron is an orderly mess of 60 woven plastic rods. The rods come in six groups of 5 and 10 groups of 3, where the rods in each group bend their way through the busy central interchange and have their ends fastened to each other with rubber bands. All of the 5-fold groups are identical, as are all 3-fold groups: the figure has dodecahedral symmetry.

If we focus only on the 5-fold groups, then these rods match the configuration in Black Hole. As described there, this pattern can be created by placing a rod along each edge of an imaginary dodecahedron and then rotating each by the same amount until they form groups of five nearly parallel rods. The configuration of rods in 3-fold groups can be constructed analogously, using a different rotation angle. So each edge of our pretend dodecahedron gives rise to two rods—one in a 5-group and one in a 3-group—and in fact, these rods touch at their midpoints (with the "3-fold" rod farther from the middle).

The 5-fold groups interlock with each other in a shape described by Robert Lang as a polypolyhedron, so named because it is a compound of multiple (identical) polyhedra. He showed that there are exactly 54 polypolyhedra. The compound formed by the 5-fold groups here corresponds to polypolyhedron number 12. Similarly, the rods in 3-fold groups come together to form polypolyhedron 20. As my sculpture is composed on multiple polypolyhedra, its name follows logically.