Cyclogon Tilings

The EarthLink zindra pages were an excellent kick-start for my exploration of the cyclocentric.  A compass and occasionally a ruler made pretty accurate patterns for exploring wiggly edged solids (mostly pillow forms), but for planning the tilings (till recently mostly quilts) I wanted a way to draw the networks quickly. So I made several full page templates.

 The one to the left prints with a 1/2 inch
border on an 8 1/2 x 11.

  To the right is a small section of a tile mosaic with a superimposed piece of the three axis circle net. I find it's near miss double wiggle a little puzzling. If not for laying the net on it I wouldn't have seen it.
This is said to be one of the mosaics sketched by M. C. Escher when he visited Alhambra in 1936. Below is the mosaic itself photographed by Patrick Gruban April 19, 2005.





The tracing on the left below were drawn in pencil on the back of a copy of the three axis network template. It shows three of the triangular cyclogon forms with just enough of the three axis network showing through to reveal how many fish (arcs, in this case 60 degrees each) define their "wiggle" (technical term). They are designated single, double, and triple wiggle triangles.
                                     
My exploration of the wiggly polygons
haven't all been three axis. To the right
is the two axis template used to produce
the single and double wiggle squares.

 This pasted up two axis template shows an experimental crossing of single and double wiggle squares which eventually led to the throw sized quilt below.

                                                          On the left is my first experiment (in pencil on the back of the three axis template) with the snub hexagon-single wiggled. The three axis net shows some when viewed larger. That happens when one doesn't make dark lines and enhances contrast later. I ran across the snub hexagon pattern (without a wiggle) while reading about tessellation                                                                   on Wikipedia.