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

CGB: Machines

In preparation for the publication of the upcoming CGB Pattern Book, we’re currently exploring a suite of mathematical models and machines to see which ones we can take into beaded, dimensional forms.

The piece below is an evolution of a hexaflexagon, and it’s called a Kaleidocycle. It’s made out of 24 peyote triangles, sewn together into a three or more sets of mirror tetrahedra. When the machine turns, it shows four distinct faces. The faces turn on themselves on clever opposing hinges (a classic engineering device called a Bricard linkage, after mathematician Raoul Bricard) and present a series of kaleidoscopic designs.

Video and beaded Kaleidocycle by Kim Van Antwerp, art director for the CGB Project.
Music: Chico Hamilton, ‘A Trip’

If you’d like to make your own, start thinking triangles and tetrahedrons, and we will be back with you soon with beautiful patterns. You can build your cycle from a flat net (ones made for folding work reasonably well) or build tetrahedra individually and assemble them into mirror sets.

And don’t forget the noble Warped Square or Hypar… this is the start of a beautiful project by Kate McKinnon and Kim Van Antwerp. Many patterns and more machines coming soon.


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.

35 comments on “CGB: Machines

  1. Kristi Switzer
    October 10, 2017

    So it would appear that I’ve missed the pre-order. Does that mean I’m out of luck or that I’ll never be able to make a beaded kaleidecycle? Please advise. I’m late to the party!

  2. Sunita Gupta
    July 19, 2017

    I just can’t wrap my head around where to put the hinges.

    • katemckinnon
      July 20, 2017

      I have a FANTASTIC pattern coming for you this week!

  3. Maxi Starr
    March 24, 2016

    I have struggled through my first kaliedocycle but it is pretty messy. Saw Cath Thomas’s on youtube. It doesn’t appear to be made of triangles or perhaps that is not clear. Do you know how I can contact her? I am eagerly awaiting my pre-ordered pattern book.

    • katemckinnon
      March 24, 2016

      Yes, it is a bit difficult without any help on the hinges. Cath’s is made in an odd lozenge way that doesn’t really fold the same way. We’ve got more coming to help.

  4. Jewel Tushka
    March 20, 2016

    Can’t wait to see this. Many new ideas and styles of beadwork.

  5. janetgunther
    March 18, 2016

    Your blog and all your work, all that you do, is such a fresh look at beading. I would love to see your group working when you get an, “Ah-ha” moment.

  6. shirley tyderkie
    February 19, 2016

    How inspiringly wonderful. Can’t wait. Love shapes

  7. Laura Shea
    February 15, 2016

    not to be fooled by the word fold in the title this isn’t an origami book:
    Piano-Hinged Dissections: Time to Fold! (Hardcover)
    by Greg N. Frederickson ; bought the book years ago and always thought I would get around to playing with beaded versions…..Laura

  8. Annie Stoltzfus
    February 15, 2016

    The Kaleidocycle is fabulous! I want to make many. I love the possibilities for roving color design.

  9. Alice Craddick
    February 15, 2016

    would love to give this one a try……

  10. Laurel Kubby
    February 14, 2016

    This is awesome!!! Will I be able to do this with my ridiculous tension? I am worried the thread will break when flexing it.

    • katemckinnon
      February 14, 2016

      I have had your amazing tension in mind as we have been examining the engineering of these machines, and yes, I do believe you will be golden.

  11. Jane
    February 14, 2016

    Can I start working on my triangles now? I am so excited to see this!
    There aren’t any special tricks, are there? I will leave them a few rows unfinished.
    I can’t wait!!!

    • katemckinnon
      February 14, 2016

      Jane, there are definitely ways that they need to go together, but if you do a series of 24 triangles, six to form each face, you will have a good start. We did our first sets of triangles with 9 beads per side (that count includes increase beads).

  12. Lisa Brenner
    February 14, 2016

    Love Kim’s hexaflexagon. It’s more bead magic! I’m going to start making warped triangles in advance of the official pattern. You and your team’s work continues to amaze and inspire me! I wish everyday included studying with you face-to-face. Hope to see you again in January if not sooner.

    • katemckinnon
      February 14, 2016

      Warped Triangles, I am intrigued! We are currently using Warped Squares and Flat Peyote Triangles, but hey, if you want to Warp a Triangle, we are on your team.
      ; )

  13. janetgunther
    February 13, 2016

    Hands down, my order has been placed for the new book.

    February 13, 2016


    I see that there are a few different books available for pre-order.

    Which one is going to have the hexaflexagon patterns in it?

    thanks jane

    • katemckinnon
      February 13, 2016

      There will be Machines in all three books, but the Pattern Book is the next out, and the one that will have the triangle-based Kaleidoscope as in this post.

  15. Rochelle Treister
    February 13, 2016

    Fabulous! I’ve just been exploring warped squares with skirts and I love the way they flex and reshape themselves with a little pressure. When I look at the photo of the warped squares attached to each other with this post, they remind me of how as young girls we would hold hands and step in and out of the circle we made and contort ourselves every which way without letting go, coming closer and getting farther away, but always attached. I’m off to make a few more and then attach them through some kind of beaded hinge that can twist without breaking. Could we make a ball joint from a larger bead that would turn inside a beaded cup that wouldn’t let it escape the joint? You’ve got me thinking!

    • Sue
      March 16, 2016

      I love imagining kids holding hands and contorting about until the hands twisted apart (I know just what you mean, but not a better way to say it!). In my mind, it quickly turns to folk dancers. Maybe warped squares in very traditional patterns? Interesting……

  16. Jeannie Galt
    February 13, 2016

    Thank you so much for all of the work you have done in Geometric beadwork. I am just starting to work through book I- and am so anxious to do a Kaleidocycle – I have most of my triangles done -it’s just the assembly that has me flummoxed.

    • katemckinnon
      February 13, 2016

      Yes, we have had a whole team on the engineering – we should have our patterns done in about a week. Hang on! Or experiment. : )

  17. Linda
    February 13, 2016

    Off to start beading tetrahedra.

    Sent from my iPhone


  18. jigsawcube
    February 13, 2016

    Hi Kate I know it’s been a while but I love this work it’s turning out to be a fabulous exploration I found a geometric origami book that I am exploring once I learn it all the oohing and waging over the work your doing is inspiring me to think about how the origami would translate into beadwork… I would love to join you at MIT and see what wonders you are inspiring there Hope to see you soon .. Thanks !!!

    Sent from my iPhone


  19. Phyllis Dintenfass
    February 13, 2016

    Will you publish the kaleidocycle triangle arrangement for those of us who don’t have mathematical model mentalities. It’s truly fabulous.

    Phyllis Dintenfass

    Sent from my iPad


  20. vee2011
    February 13, 2016

    Reblogged this on vee2011.

  21. Deanne Anderson
    February 13, 2016


    Sent from my iPhone

  22. BarbaraBriggsDesigns
    February 13, 2016

    Very cool!!!

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