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Home > 3D-XplorMath

Hopf Fibered Linked Tori

"Hopf Fibered Linked Tori," by The
3DXM Consortium


The Hopf map maps the unit sphere in four-dimensional space to the unit sphere in three-dimensional space. The four tori linked in this image are made up of fibers, or pre-images, of the Hopf map. In this visualization, each fiber has a constant color and the color varies with the distance of the fibers. Any two of the four tori are linked, as are any pair of fibers on a given torus. See more surface images on the 3D-XplorMath Gallery.

--- adapted from "Hopf Fibration and Clifford Translation of the 3-Sphere," by Hermann Karcher

bi-pentagon.jpg Breather.jpg Hopf-FiberedLinkedTori.jpg MandelbrotSet.jpg normal_hilbert_square.jpg