Phase Flip Side Slip

                                                                                                             Far from a complete list, below are a few of the more obvious cyclocentric polyhedra in phase flipped (side slipped) networks. Beginning with the triple wiggle rhombi (hopefully plural for rhombus). As you may have noticed I didn't wait for water-jet access, nor let the lack of a commission slow my quest for cyclocentric symmetry (and tile work). As much as I like the blind two headed goose look of the triple wiggle rhombus, relative to recent cutting experiments, I believe it would take about thirty minutes each to cut these with a diamond side-grinder. I don't like them that much. But wait, there's more!

Next up the double wiggle rhombus. Challenging yes, but it only takes about 9 minutes each piece to achieve this effect. Color alone doesn't account for the apparent shape disparity of the phases. I was toying with a color palate I had in mind for a tile/travertine back-splash. Very weird, the chocolate and strawberry ones (they seem more pink than purple to me) look like they're climbing while the mint and café au lait ones look stacked ( like vertebrae).

Finally something that looks good in two
colors. As visible through the truth window,
these double wiggle triangles (unlike those from the Alhambra photos)
have two fish in every curve. It takes red and white in both
phases to accomplish this wiggly, mostly
non directional, almost checker like pattern.

The phase flipped, side slipped, single wiggle triangle is one of my favorites. While structurally similar to the grain of the phase flipped, double wiggle triangle net, it however has a very directional appearance. This example seems to flow up to the right. Test cuts revealed a minimum edge length of about 3 1/4 inches to be possible with fair accuracy. Like the sewn ones, in tests the hand cut arrays were surprisingly fault tolerant. I look forward to some practical applications.


                                                                                                                           

 




 So far this is the most appealing two color arrangement I've come up with for the phase flipped, side slipped, single wiggle rhombus. The same wrap around the dot look also works well for the phase flipped, single wiggle square net. However with single wiggle squares, I think more colors even if they're subtle (like several celadon shades) would work better.

I'm not done with this, but I'm done for now. I hope some of this is useful.

Trust Your Heart

"Trust Your Heart To Lead You Home" is a triptych carved on cherry wood panels. This mosaic mock-up is a variation on the third panel, and is my fourth effort at a feasible cyclocentric mosaic in tile. It contains samples of  five polygons not commonly seen in tile in five networks similarly underused, these polygons have all been test cut (with diamond tools) in the sizes necessary to produce this image for a back-splash 41 5/8 in x 87 in.  

These examples represent the smallest pieces I was able to cut consistently. Quite a number of them just broke from the strain, and more than a few were backwards (the wiggle has a direction). It wasn't until later that I realized those backwards pieces were the key to an even odder group of symmetries. I was moving them around wondering just how one might join lefty wiggles to righty ones. I had to flip some over because so far I had no place for out of phase pieces. That was before I discovered "phase flip, side slip".
Applied to the triple wiggle triangle window, these phase flipped triangles don't just wiggle they crawl. The effect on the other cyclocentric polyhedra is no less pronounced.

This is the post that made this blog necessary. Posted first on LinkedIn, then on experimentalQuilting , this is where I'll be exploring "phase flip side slip" and whatever other new cyclogon flavors I can uncover.   

first posted on LinkedIn Dec10,2015

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.                
                                                          

Cyclohedra Indeed

Ok, First things first. I have alluded to the mysterious "Cyclocentric  Polyhedra pages and admited to having a copy of them. So here they are.  

 

It tickles me to see this awesome content once again available. May Google and Blogspot keep it safe for us all. I'm pretty sure this earthlink post relates to the original source of this excellent material.
  
first posted on pillowhedra.blogspot.com. FRIDAY, DECEMBER 6, 2013

The Pursuit Of Cyclocentric Symmetry

My own cyclocentric  pursuit began with the curvy wall project.

Pinning down the ideal shape for this wall and trail was surprisingly challenging.  After days of photographing, measuring, and driving stakes in their back yard, my clients forwarded me a link to an Earthlink post by zindra it was labeled sacred geometry. The twelve pages revealed how to use circles to generate rippled edged polygons, and showed some solids made with the curvy edged faces. The idea of generating shapes from a series of circles proved very useful. The path we settled on was a series of circular sections draped across the hillside. A curved stair at the far end leads up to a more gently winding upper path that rejoins the lower path just before the beginning of the  wall. At that time the networks and wiggly polygons were more than I could take in, but I found it interesting enough to print it out to explore later. Good thing, when I dug up the pages 8 years later Earthlink was gone. My stashed printout was all that was left of zindra's earthlink post. I have enjoyed exploring the potential applications of the cyclocentric patterns, but I'm hoping the pillow forms and quilts are just a warm up for some heirloom floors or maybe even a driveway or patio. The networks are demanding, and the polygons tortured, but they stagger along filling two space like nothing I've seen short of M. C. Escher. Water jet cutting should make these patterns possible even for a floor or shower. 
first posted on LinkedIn October 20, 2015