### 4D sculpture with a 3D shadow

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**Media:**Article]

I won't pretend to fully understand how a 4D object works, but the sculpture and the article remain quite fascinating to me. There is also a Flash Animation of the sculpture. Beautiful.

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.

"Four-dimensional models are useful for thinking about and finding new relationships and phenomena," said Ocneanu. "The process is actually quite simple -- think in one dimension less." To explain this concept, he points to a map. While the Earth is a three-dimensional object, its surface can be represented on a flat two-dimensional map.

Link (via Boing Boing)