The 24-Cell in 3-D

The 24-cell is a mysterious regular polytope in 4 dimensions, in that there’s no analogy to a Platonic solid. Since 2005, the campus at Penn State has featured a sculpture based on a 3-dimensional projection of this 4-dimensional object. The sculpture, known as the Octacube, was designed by Penn State mathematics professor Adrian Ocneanu. The sculpture was sponsored by Jill Grashof Anderson in honor of her husband, who was killed in the September 11th attacks.

Penn State has put out a shorter and longer article on the sculpture.