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Doing some reading online about tessellations; found this little snippet from this site.

The dual of a tessellation is formed by connect the centers of the shapes in a tessellation so that these segments do not pass through a vertex of the tessellation. The dual tessellations of the regular tessellations are themselves regular tessellations. However, the duals of the semi-regular tessellations are not semi-regular tessellations.

So, now I know the official way to discover the dual of the tessellations I am folding. Helpful!

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