In- and Outside the Torus

	This image depicts the three-dimensional projection of a torus in four-space. Bands on the torus have been removed to make it possible to "see through" it. Banchoff's description of the torus and the three-sphere provides more information about this image, and includes several MPEG movies of the torus rotating in four dimensions.
	The artist's comments
	The mathematics behind this image
	Movies of this object rotating
	interactive versions of this object
	A larger version of this image (160K)
	Artist and medium
	This image appeared originally in the book Beyond the Third Dimension, part of the Scientific American Library. You can purchase it on line, or read a short review of it.