# The Knot Pattern on the VE

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 4 x 4 = 16 edges of the VE. The VE has a total of 24 edges. So there are 24 - 16 = 8 edges of the VE "unused" in the Pattern Knot.

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)?