4D sculpture with a 3D shadow

Alex sez, "Adrian Ocneau, math prof at Penn State, designed this mathematical sculture that revealed a 3-d shadow of a 4-d object."

In the three-dimensional world, there are five regular solids — tetrahedron, cube, octahedron, dodecahedron, and icosahedron — whose faces are composed of triangles, squares or pentagons. In four dimensions, there are six regular solids, which can be built based on the symmetries of the three-dimensional solids. Unfortunately, humans cannot process information in four dimensions directly because we don't see the universe that way. Although mathematicians can work with a fourth dimension abstractly by adding a fourth coordinate to the three that we use to describe a point in space, a fourth spatial dimension is difficult to visualize. For that, models are needed.


(Thanks, Alex!)

Update: Here's a Flash animation of the sculpture (Thanks, Bonthon!)