an open source architectural beadwork project from Kate McKinnon and a worldwide team of innovators

Background for PodCast BeadAlong

Almost 7 years ago I held a necklace of geometric stars made by Stacy Creamer, built to a design by Jean Power. Each star was made of five Warped Squares. I was entranced by the small miracle of the Warped Square; here, at last, was something that Didn’t Fit. I spend much of my life observing those telltale signs of complexity, things that Don’t Fit.
I now know these mysteries as Hypars, or little hyperbolic planes. They are everything. They can even be Deconstructed, like in these earrings by Kim Van Antwerp. This is like.. intersecting hyperbolic planes. They might lead to shocking thoughts if worn near the brain.
Flicka pair
Once I got going making my own geometric pieces, I became fixated on why the sturdy, reliable Flat Peyote Triangle seemed so much like the elusive Warped Square. Why herringbone increases looked exactly like decreases, even though they went on completely differently. I was so distracted by these questions that I found it difficult to comprehend the forms. My Triangles were oddly full of errors.
People asked me for most of last year why I wasn’t putting out a pattern book. Why was I, an artist and writer, instead inside the Skunk Works, or at MIT, or chasing around after topologists, asking about Clifford algebra, talking about quantum propulsion. WTF.
It wasn’t really that odd. I wanted to understand before I published this time. I mean really understand. And I was beginning to realize the history of some of the forms I was seeing, and their implications.
Franklin Martin Cycle 3
The Kaleidocycle, for example, was neither an invention of beaders nor of origami artists. It is a classical arrangement of Mirror Tetrahedra (which answer to no man or woman) in a linkage. (Cycle above by Franklin Martin).
The linkage was described by Raoul Bricard, a French mathematician, at the turn of the last century – along with many other machines and kinematic chains of nature that are still being studied. The cycle is an organic, essential machine that Nature knows well how to make, and you might see virus arranged in such a ring, or realize that social patterns resolve to the same kind of eternal rotation.
The crafting of Hypars into Star forms is also done by Nature. Origami artists make them, and computational origami studies the many arrangements they (and other hyperbolic, folded, pleated or energetic forms) can make. Erik and Marty Demaine name their arrangements of Hypars by how many “hats” they make put together . Everyone has niche terminology for the forms of Nature, but none of us own them.
I think this is really worth contemplating when one hears people talking about how they discovered, created, or own a pattern, or arrangement of shapes. To use words like that, a person really has to do some digging.  Beaders did NOT invent any of these shapes. But figuring out how to best make them in our materials is something, for sure. And I do feel we can contribute to their understanding. (Photo Erik Demaine with a folded paper Hypar, you can find the pattern here.)
. .
The reason that I began in this field is that beading is one of the oldest things that humans do. And only humans do it. This fascinates me. The patterns, counts and shapes that we work with are elemental, universal, and they are bigger than mathematics, because they describe pure form.
Topology has been helpful, as has a more rigorous study of geometry. I can now see that the inside space of a Rick-Rack or an All-Wing is just a folded up polygon. A Six-Wing, in a flat representation, is like a dodecagon, with half of its legs folded in. And in real life, maybe it’s like a dodecahedron, folded into 12 legs, 6 up and 6 down.
You know, during its construction, the 6-Point Rick-Rack makes each of these shapes:
Screen Shot 2018-03-21 at 8.18.11 PM
So. When I try to understand how to make the thing:  if the Rick-Rack is a folded up 12-gon, then what does the middle look like? A tinier version of the same. That’s where we should start, then, not with the outside line of the completely expanded form. Nature makes folded, spiky things all of the time. Look at this carrot seed!
Yes! It makes a carrot plant. Virus is spiky, too, and waves and frequencies represent as zigged lines. This is very elemental stuff. (Image by Rob Kesseler.)
Nature has a kind of symmetry that cannot be denied.
So what I was hunting all of this time when I was looking for the smartest way to make a Zigged form was actually the middle of a Rick-Rack, the doughnut hole, as it were.
It turns out to be an even tinier spiked form; a tiny All-Wing. It looks like this, and it’s easy to see, and even easier to make.
Podcast web
And it’s our first Bead-A-Long.
Join us tomorrow to make your own tiny little All-Wing, the PodCast Bead.

About katemckinnon

Kate McKinnon has devoted herself to the study of how things are done, and how they could be done better. Find her at or on some city street, walking fast, smiling at strangers.

7 comments on “Background for PodCast BeadAlong

  1. puzzledeb
    March 23, 2018

    Re: [New post] Background for PodCast BeadAlong

    Thanks for all of it.  Everything you have done for this project.  And for needing to understand. That makes everything better. Debby

    Wednesday, March 21, 2018, 5:32:21 PM, CONTEMPORARY wrote:

    katemckinnon posted: ” Almost 7 years ago I held a necklace of geometric stars made by Stacy Creamer, built to a design by Jean Power. Each star was made of five Warped Squares. I was entranced by the small miracle of the Warped Square; here, at last, was something that Didn’t”

  2. Maureen
    March 22, 2018

    Thank you, Kate McKinnon, for re-kindling my high school love affair with geometry.

  3. Kathi
    March 22, 2018

    I can’t wait to get started! Would you be willing to identify the pink, peach, lavender, and green delicas in the above photo (if possible)?

  4. Cathy
    March 22, 2018

    I have your book and am too lazy to dig it out. 😊

    I noticed that the ring is not made out of delicas. Did you use druks in it?

    Thank you

    • katemckinnon
      March 22, 2018

      Size 8 round beads, and the first round of increase beads is double-square-stiched to the Circle Start. It makes a really stable, self-organizing form.

  5. Julie
    March 21, 2018

    I am not a mathematician, but I do see nature mirrored in your beaded work. Excited to try out these marvelous shapes!

  6. Gemma Williams
    March 21, 2018

    Know. What I’ll be trying to bead tonight

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