While exploring various daul dynamics of the Platonic polyhedra (click here to go to this study) I discovered that the Pattern knot matches the initial position I was using for the cube/octahedron dual pair.
Here is the Cube/Octahedron initial position I was using.
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Here is how the Pattern knot appears....
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Note that there are 4 of the cube (pink) vertices and 2 of the Octahedron (green) vertices unused. (That is, which the Pattern knot does not pass through.)
This suggested to me that another Pattern knot can be defined by the unused vertices.
To do so requires that re-use of 2 of the Octahedron vertices.
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Here are both knots together covering all vertices.
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But not all orange struts are covered. There are 8 struts left uncovered by the knot edges.
To cover all the struts requires 2 more Pattern knots.
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At the moment it is not clear what the significance of this is.
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