The "VE", which stands for "Vector Equilibrium", is really the Cuboctahedron. I'll show how the edges of the VE define Lynnclaire's Pattern Knot.

First, here is a picture of the VE inside a cube.

The Pattern Knot can be thought of as 4 intersecting "arcs". For the situation described here, the "arcs" are made from 4 line segments each.

Here is the first arc of the Pattern Knot drawn in red.

Now for the 2nd arc in a slightly lighter red color.

The 3nd arc is now drawn in green.

And Finally, the 4th arc in pink.

Each arc consists of 4 edges of the VE. And with
4 arcs all together we have used

NOTE: I (and others) have shown elsewhere that the knot can be drawn using 2 straight edges per arc. I have recently shown how to draw the Pattern knot on the faces and edges of a cube which results in 3 line segments per arc. Now we have the Pattern Knot drawn on the VE edges with 4 line segments per arc. What will 5 line segments per arc correspond to (if anything)?

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