I've always been fascinated by the similarities between mathematics and art. (Although, anyone that knows me will agree that I am staggeringly inept at anything involving numbers.) It's the way mathematics expresses itself symbolically that intrigues me—numerical prose used in an attempt to describe the indescribable. Math and art often share the same goal: to make the seemingly unquantifiable become more lucid through using a series of symbols and analogies. 

Through mathematics and the various arts, elusive beauty can be discovered and shared via a representative. Sometimes this representative is a symphony, an oil painting, a poem, and sometimes it is a sculpture depicting the three-dimensional "shadow" of a four-dimensional object. I won't try to describe the Octacube any further at this point, but will strongly suggest that you take a look at this article describing its design and significance. I recently came across this page (though the sculpture was unveiled in 2005) while searching for something else, and was immediately struck by the piece's beauty, both as a work of art, and as a tool of mathematical representation.