# Geometric Bead Designs and Origami: Journeys in Math and Art

Are you an analytical, logical math whiz or are you the free-spirited, artistic type? I don’t know about you, but I’m annoyed by questions framed this way. The seemingly innocent query above actually has an underlying bias, assuming that if you’re good at one thing, you could never be good at another – and that’s not the case at all.

We are drawn to pattern, proportion, and rhythm.

What we find artistically pleasing is often embedded in the logical rules of the universe. Think of the precise growth patterns of plant leaves, the efficient folds of a bat’s wings, the golden mean of the snail shell, and the proportional truths in music. Rather than existing at opposites ends of the spectrum, math and art are beautifully intertwined. This synthesis in ourselves is easily seen in our affinity for pattern, balance, repetition, and variety.

Sue Jackson and Wendy Hubick incorporated colorful cube and pyramid beaded beads in this bracelet, Charmed, I’m Sure. Find it in the eBook 12 Beaded Bead Projects to Make.

## The Beauty in Order

As far as math classes went, geometry was my favorite in school. It was so visual, so clear. I even loved the proofs – those satisfying little logic puzzles solved one step at a time using known geometric truths.

Long before high school geometry, I was an origami enthusiast. I loved the dimensional transformation of the paper from flat to formed through a series of folds and maneuvers. As a kid, I did origami with my mom, who taught me how to make flapping birds and jumping frogs and even inflatable snails. As I got older, I tried more intricate designs, including modular origami.

Modular origami is comprised individual units that can be tucked into the pockets of other units, resulting in complex interlocking structures. From six-piece cubes to a variety of polyhedrons with dozens of modules, this sort of origami brings geometry to life in a very tangible way.

This model is made up of 60 units. You can see how the points form groups of five (pentagons), groups of four (squares), and groups of three (triangles), creating a spiky variation of a rhombicosadodecahedron.

It’s no surprise that when I started beading (which was not all that long ago), I was drawn to the dimensional, geometric shapes that beads could form. I immediately noticed that Cindy Holsclaw had a whole video called Geometric Beaded Beads: From Cubes to Dodecahedrons – how very much like origami!

It turns out that Cindy is not only a bead artist but an origami master with a doctorate in biochemistry and molecular biology. Her math-and-science background features heavily in her artistic endeavors, evidenced by her geometric modular origami and fabulous beaded molecules, such as her chemically-accurate alpha-endorphin. Even her website name BeadOrigami.com captures that unique overlap between origami and beadwork.

Cindy Holsclaw shows examples of Platonic solids. From left to right: icosahedron, dodecahedron, octahedron, cube, and tetrahedron.

## Geometry with Cindy Holsclaw

Now that I’ve learned popular stitches like peyote, herringbone, and brick stitch and flirted with the exciting possibilities of right-angle weave, I decided I was finally ready to dive into Cindy’s tutorial on polyhedrons. I was intrigued by her introduction, in which she uses dice to give us a tour of the five Platonic solids – the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

Defined as a convex shape made up of flat faces, each of the five types of Platonic solids is comprised of identically shaped faces, with the same number of surfaces meeting at each corner. For example, a cube is made entirely of squares, always with three squares connecting at each vertex. Likewise, an octahedron is made up of all triangles, with four joining at each corner. To see this visually, check out the 3D animated models of these five solids on Wikipedia.

In her video, Cindy focuses on cubes and dodecahedrons – two shapes I love in origami – so I was excited to get started. Though I wanted to dive straight into the dodecahedron, I told myself to be smart and start with the cube. That turned out to be a wise decision. To make what is essentially one unit of cubic right-angle weave, I used large beads, one per side. Then I followed along as she demonstrated making a cube with bugle beads, using size 11 seed beads as decorative corner covers. I like the look of the bugle-style cube with corner-cover beads, though I kept accidentally forgetting to add them in the right places. I particularly love her “bubbly” cubes made with drop beads.

Cindy teaches a basic dodecahedron with 30 crystals before showing lots of fun variations.

For the dodecahedron, made up entirely of pentagons, I broke out my 6mm Swarovski crystal bicones. (Fun fact: In Greek, do means “two” and dekas means “ten,” thus a dodecahedron refers to a 12-sided shape.) Following Cindy’s advice about color-coordinating my crystals to keep me oriented, I found the dodecahedron more straightforward than I expected. It’s very much like right-angle weave, but with five beads to a side instead of four. It’s similar to the mental switch you make when creating three-sided units of triangular weave.

Left: My 30-piece origami ball, in which each group of five units forms a pentagonal star. Right: My 30-crystal dodecahedron, in which each group of five beads forms a pentagon.

I managed to form all 12 pentagons and close up my shape, but my beadwork was too flexible, caving in on itself. Determined to make it work, I did as Cindy recommended and reinforced the thread paths with excessive amounts of FireLine (affiliate link) until my “crystal ball” took on a sturdy, convex shape. Now it’s the perfect embellishment for my rearview mirror, casting sparkly rainbows throughout my car. I would like to try Cindy’s final variation as well – a dodecahedron using bugles and corner-cover beads – but first I’ll need to perfect this technique with cubes.

Following Judy Walker’s book The Beaded Sphere, I completed half of a seed-bead dodecahedron.

## Beaded Spheres with Judy Walker

Another geometric project that I’ve been working on is from Judy Walker’s book, The Beaded Sphere (affiliate link), a title that naturally jumped out at me and forced me to take it home. She starts off by teaching her readers how to make a single hexagon with seed beads, using six per side and adding rows of peyote stitch to create a distinct shape. These individual hexagons (or pentagons or triangles or squares) can then be linked together to create flat or spherical beadwork.

In a soccer ball, each pentagon is surrounded by five hexagons.

Immediately intrigued, I began making a few hexagons, thinking I would whip out a soccer ball shape known as a truncated icosahedron. But then it dawned on me that I would need 20 hexagons and 12 pentagons in total, something that seemed like an enormous feat, especially considering that I’m not a fast beader.

I readjusted my plan, aiming instead for a familiar dodecahedron that required just 12 pentagons. I have been adding a pentagon every once in awhile and creating the “hinge” to attach it to the rest of the beadwork, as Judy instructs. So far, I’ve completed half of it, and eventually it will make a beautiful Christmas ornament.

Oh, the shapes we can make! Two-dimensional triangles, squares, pentagons, and hexagons can be combined in lots of exciting ways to make all kinds of shapes, whether you know their names or not. Here’s a little chart in case you want to experiment:

There are all kinds of geometric inspirations you can draw on for your beadwork, from flat, bold shapes to dimensional beaded beads and even structural ropes and spirals.

Get the eBook 12 Beaded Bead Projects to Make for creative ways to play with dimension. Clockwise from top left: Swirl Beaded Bead Necklace by Diane Fitzgerald, Opulent Octahedron Necklace by Cindy Holsclaw, Carousel Bracelet by Laura Andrews, and Ornamental Beauty Beaded Bead by Maria Teresa Ferreira.

Whether we admit to liking math or we rely on our instincts for design, whether you work with beads, paper, or something else, geometry binds us to an exciting world of beauty and order. Hopefully some of these projects have planted a seed for your next design.

Go be creative!
Tamara Kula