| Search results - "linked" |
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
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"Eights," by George W. Hart (www.georgehart.com)This six-inch diameter paper sculpture is made of sixty identically shaped parts. Parts of any one color form a type of tetrahedron, and there are five such, deeply interlocked. No glue is used; they parts just hook into each other. I call this type of design "modular kirigami". It took me about four hours to assemble after several hours of false starts and figuring out how to do it. I generated a computer-rendered view down a five-fold axis. The "8"-shaped parts each link with many others. So they could not be made as single pieces of paper unless they were glued or taped together after being linked. But I wanted to be a purist and use no glue or tape, so I designed the parts as two overlapping "3"-shaped pieces.
--- George W. Hart (www.georgehart.com)
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"Arabic Icosahedron" by Carlo Sequin, University of California, BerkeleyMoorish patterns found in the Alhambra often depict lattices of interlocking knots. Here such a pattern composed of interlocking trefoil knots has been wrapped around an icosahedron. Each of the 20 faces is replaced with a trefoil knot, which interlocks along the triangle edges with three adjacent trefoils. The exact nature of the linking between adjacent trefoils leaves some freedom to the designer: In the simplest case two adjacent trefoils interlock with just one lobe each. In the "Arabic Icosahedron" they are linked with two lobes each, resulting in a much tighter meshing. --- Carlo Sequin
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"(10,3)-a Twice," by George Hart, Stony Brook University, Stony Brook, NY (2008)Nylon (selective laser sintering), 3.5” x 3.5” x 3.5”. "This is a sculptural interpretation, made by selective laser sintering, of two copies of the (10,3)-a lattice. Modern layered fabrication processes allow the construction of two interlocked components which are free to move slightly relative to each other, within the constraints of their being linked. The two copies are congruent, though mirror images. Each interpenetrates the tunnels of the other in a surprisingly complex manner. The 5x5x5 selection from the infinite lattice was made in such a way that the sculpture can stand vertically on a corner. See more works at http://www.georgehart.com." --- George Hart, Research Professor, Stony Brook University, Stony Brook, NY
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