Cheops Configured Triaugmented Triangular Prism

The Cheop's variant, double wiggle cyclocentric,

 triaugmented triangular prism pillow was actually
 completed back in January. I kept hoping to get a nice cover made, but I got started coding (the Flatware County Diet board game (still hanging fire on scratch.mit.edu), then casting moss growing concrete (the Hairy Hendecahedra Project, at blocklogic.blogspot.com), and then most recently experimental quilting. My current project, a double wiggle triangle cyclocentric cylindrical quilt (bolster pillow upholstery) is a continuation of a series of cyclocentric quilting projects at experimentalquilting.blogspot.com   .  

CYCLOCENTRIC SNUB SQUARE ANTIPRISM

This lozenge shaped pillow uses the same single arc cyclo square and triangle polygon patterns used in the cubocta pillow. This time the nine inch edges produced a pillow approximately 21 inches in diameter, and about 11 inches tall. This would have been an interesting pillow without the wiggle.  

 I'm thinkin it's time for the next level of cyclocentric complexity.  To add an additional dimension to the next pillow, the tri-augmentations to this triangular prism include proportions derived from the Pyramid of Khufu. These are intended to enhance its psionic properties, but mostly it'll make the points shorter and more separate looking. Once again Poly was the source of the clip art to the left, and provided the peel I used for the model on the left below.

 Shortening the pyramids means the addition of a second set of wiggly edges. To make all this arithmetic a little simpler, I decided to go metric. The size I've settled on has a base edge 30 cm (12 inches) long , and angled edges of 28.5 cm. In case you're trying a different size, the page below was the most readable psionic pyramid formula I found.

Finding  the unknown height of my 30 cm square pyramid was just a warm up for finding the radius for making the threefold networks needed for my wiggly polygons. Below are two stages of my templates showing how to begin the net with a single center line, and demonstrating that the height of the triangle made by the points equals three times the radius of the circle that makes it. The two arc wiggle is another level of challenge, and I still have to cut these out and piece together the side templates. I will use the 30 cm one to make the top-bottom template first.

WIGGLE DISCOVERS ARCHIMEDES CUBOCTAHEDRON IS NEW AGAIN

I was scrolling through the shapes in Poly for some other interesting shapes that would use triangles and squares the same colors as Madi's pillow.
Cuboctahedron, in the Archimedian Solids looked cube-simple. At fourteen sides it looks a little simpler than it really is. In it's cyclocentric form, this model has a fairly high wad-factor. I unfortunately got lost and had to rip out a number of well sewn seams before I finally got it straightened out. I referred often to a paper peel-model from the printer. Models may not be good for much but they've  really gotten me craving to see one that's built soft, stuffed full enough to see what does as it puffs toward an even more spherical shape. The edges on the cyclocentric cuboctahedron and those of the fleece gyrobifistigium were both nine inches, so I had make new templates.

   I never could run the networks very far, but looking at the sample nets on the cyclocentric pages
I managed to ape enough on my patched together poster board to get some accurate seeming patterns.

 The denim triangles saved the day when I ran out of canvas and had to use old jean legs.

    I was looking for cubocta look-a-likes, when I found the snub square antiprism, J85 in the Johnson Solids. With twenty six sides, twenty four of them triangular it's got lots of edges to wiggle. Ouch, that's twelve more than I bought fabric for. Once again, a more careful examination would have saved time. It looks like after Christmas before this reveal.

Intriguing Yule Tide Stellation

A pentagram, bisected, flipped, and folded makes a much more interesting star, but only in 3dimensions. Consider it an excellent excuse to make a simple model that looks exceptional.

The inner pillow form began as a foam cube sawn into roughly the correct shape with a serrated knife. The foam  was then layered over in coarse stitched cotton batting, with some loops penetrating to the center of the opposing face.The pillow form cover is white satin, and so a little fragile.

I feel like I got a head start on this one already. I've seen the template work twice now, and the shape is one I want laying around in canvas. I'll tack on the completed shell pix as soon as I've made it.

Tension Builds Where 2 Meets 3 On A Bias

The marking went a little weird. Canvas doesn't seem to stretch much, but carefully marked with templates mated to their reflected shape were gaining or loosing a quarter inch or more when pinned from one end or the other. All this chasing and pulling of the edge itself distracted me for a seam or two from the ground rules of fabric, it usually stretches but seldom evenly. Point control using pins had gotten me trough walking fabric before, but hitting one is easy and several kinds of a drag. Starting at the ends and working in potential errors are absorbed through compression or stretch over the whole edge. I liked these clamps better than pins. No poking accidents, and they're easy to not sew over.

 There's nothing mysterious about cutting on the bias, but it's been awhile since my last polyhedra pillow. Strange as they felt in the sewing, they came out great. They're about 14 inches in diameter, natural cream canvas about as thick as my jeans. The canvas makes such a tough pillow form they'll keep for now.

I'll probably get cyclocentrical some more later, but for now I've got a couple of more odd fish to fry first.

Rhombic Dodecahedron Gets A Wiggle On

Quoting from zindra on earthlink in 2006 "there is, however, a subtle twist to this picture, both literally and figuratively, in that another family of regular volumetric polyhedra exists, heretofore overlooked, which can be generated from the circle alone using only a compass: the cyclocentric polyhedra."

While the weathered tumbled travertine of the garden rhombi looks seed or even nut-like, even this first proof of the cyclocentric rhombic dodecahedron definately has a wiggle on

. The grocery store compass I have is plastic and looks clunky, but it has a screw to lock it tight. This eight inch single wiggle edged rhombus should yield a pillow approximately 14 inches in diameter.

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.  

 

I have not yet even read all these pages and may not, still 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.