The octacube is a large 3-dimensional mathematical sculpture illustrating a 4-dimensional structure (the 24-cell) in the Galois theory of operator algebras.
It was designed by Adrian Ocneanu, a professor of pure mathematics at Penn State, which commissioned the sculpture. Ocneanu was also an International Mathematical Olympiad gold medalist in 1974 by recording a perfect score for his native country, Romania.[1]
A feature article on the sculpture appeared in the March 2006 issue of the popular journal Playboy.[2]
A more complete technical explanation[3] of the sculpture, including how it came to be made, how its construction was funded and its role in mathematics and physics, has been made available by Penn State.
In addition Ocneanu has provided his own detailed commentary.[4] The octacube provides a physical means of visualising quantum symmetries associated with exceptional structures arising in the theory of subfactors, initiated by Vaughan Jones.