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.