A flat ribbon is tied in a figure 8 knot and pulled as tightly as possible in the X,Y plane. The red and white sections in the Z direction could all be reduced to 0 length to fully close the knot, so they don’t affect the knot being “pulled as tight as possible”, nor are they required to have the same width as the blue ribbon sections. They are retained only to show the layering of the blue sections that are parallel to the X,Y plane. This model does not limit the fold angles to 60 degrees as my earlier model does.

Although some struts and panels do not fall on standard vZome orbits, I was pleased to discover that this fully tightened version of the knot could still be generated within the golden field, meaning that all of the vertex coordinates are rational multiples of one plus the golden ratio. Surprisingly, all of the numerators are less than 10 and the greatest denominator is 2.

This model was generated with vZome. The vZome file is included in the zip download of this model.

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published a year ago

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Figure 8 Knot Tightened Completely 3D Model

Figure 8 Knot Tightened CompletelyYour model is disabled. For more details go to Edit properties3D Model

Figure 8 Knot Tightened Completely
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3D Model