Chaim Goodman-Strauss

The tubing in this sculpture all lies along circles (or lines, circles of infinite radius). In fact, we can fill all of space continuously with each color of circle — these are each stereographic projections of a Hopf fibration, a division of the hypersphere into circles. The red, green, and blue fibrations are oppositely handed from the yellow one, and they all meet at right angles. In the hypersphere, these circles have symmetry denoted ±[TxC_6] in Conway's notation --- this sculpture is one of a series illustrating many of these symmetries. This is part of a larger project to illustrate many other symmetries of the hypersphere.

Using the principles outlined in the description of other submitted piece, these pieces show several other symmetries of the hypersphere, all subgroups of the symmetry of the compound of two dual 24-cells, in objects such as a compound of two compounds of three 16-cells; a compound of three hypercubes; or the double covers of Cayley graphs of the rotational symmetries of a tetrahedron.