Kazunori email these photos of a beautiful bead model of (2,9)-Carbon nanotube torus knot (CNTTK) he just made the other day. To make the structure more clearly, I also use the Grapher to create the corresponding torus knot.
This one is hard. You need to be careful about the spatial arrangement of pentagons and heptagons.
If you are already familiar with tori and helices, you might want to give a try. If not, you should become with these two families of structures first!
1. Face-sharing. The result is a straight tetrahelix, or the Boerdijk–Coxeter helix;
2. Edge-sharing. Even number of tetrahedra linked in this way to form a loop, one get the Kaleidocycle. Of course, with many tetrahedra linked in this way, one can create almost any knot, including torus knot. I made a trefoil knot linked this way before.
3. Vertex-sharing. Tetrahedra linked in this way will be very flexible. Since each tetrahedron has four vertices, there are infinite number of possiblities with vertex-sharing.
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5 comments:
I would like to know how to create one of my own....
This one is hard. You need to be careful about the spatial arrangement of pentagons and heptagons.
If you are already familiar with tori and helices, you might want to give a try. If not, you should become with these two families of structures first!
I wonder if this could be achieved with tetrahedron-chain. Marvelous design!
I wonder if this could be achieved with tetrahedron-chain. Marvelous design!
There are three ways to link tetrahedra:
1. Face-sharing. The result is a straight tetrahelix, or the Boerdijk–Coxeter helix;
2. Edge-sharing. Even number of tetrahedra linked in this way to form a loop, one get the Kaleidocycle. Of course, with many tetrahedra linked in this way, one can create almost any knot, including torus knot. I made a trefoil knot linked this way before.
3. Vertex-sharing. Tetrahedra linked in this way will be very flexible. Since each tetrahedron has four vertices, there are infinite number of possiblities with vertex-sharing.
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