Colouring-in: Dualing

Dualing

This pattern is the third generation triangle pattern we created on the

Edge Replacement page.

To form a "dual" we place a point in the centre of each polygon of the original pattern and then add lines joining the points in adjacent polygons. The image below (left) shows the result of applying this transformatin to the image above. The second image below (right) shows relationship between the two patterns, red lines being the original pattern and black ones the dual.

Note that all the shapes in the dual are pentagons. Generating patterns consisting entirely of pentagons was the original purpose behind this idea.

Combining Dualing with Edge Replacement

We can apply the edge replacement operation to the dual pattern producing this rather interesting object.