origami papercraft polyhedra

Five Interlocking Tetrahedra

Five Interlocking Tetrahedra - Angle 1Five Interlocking Tetrahedra - Angle 3Here are a few (unfortunately low-quality shots) of a modular origami implementation of five interlocking tetrahedra. This model uses Thomas Hull’s design. The joins are a bit sloppy, but it holds together nicely.

Modular origami is quite relaxing, very much like knitting. Once you have mastered a basic pattern, you can just disengange your brain and let your hands do the work. For larger constructions, in fact, it is extremely important to have something else distracting you from what might otherwise become intolerable tedium. Then, after you’ve constructed all your modules, comes the fun part: stitching everything together into the finished shape. This design, in particular, is a bit of a brainteaser; you have to carefully puzzle out where each strut goes, under or over. The final result is satisfyingly impressive.

papercraft polyhedra

More Modular Origami

Display window with modular origamiHere are a few more origami polyhedra that I had lying around the house. The white, central polyhedron is an isocehedral degree 3 type I geodesic sphere. (As with the degree 5 version in a previous post, I used a computer to get the chord factors right.)

Just above and to the right of the geodesic sphere is a rhombic triacontahedron; you may recognize the shape from the 30-sided polyhedral dice sometimes used in role-playing games. Continuing clockwise, the picture shows a flower-colored snub dodecahedron; a smaller rhombic triacontahedron; two snub cubes; an isocahedron; four interlocking tetrahedra with a small rhombic cuboctahedron in front of it; a spiked rhombic cuboctahedron; a cube with decorated faces; and another isocahedron.

Making these is quite relaxing, much like knitting. As they get larger, though, the level of obsession needed to see one through to completion grows geometrically.

papercraft polyhedra

Geodesic Origami

Isocehedral Degree 5 Type I Geodesic Origami - On DisplayHere’s a geodesic sphere made from paper – the largest origami construction I’ve made so far. It’s made using a dirt-simple folding technique called ‘snapology‘, based on strips of paper rather than squares. To be precise, these images are of an isocehedral degree 5 type I geodesic. The first challenge in putting one of these together is getting the lengths of all the edges (the chord factors) correct. I used the GPL’d DOME package to calculate lengths, and then used a few Python scripts to generate printable SVG cut-and-fold designs for the strips. The second challenge is the insane amount of cutting and folding.

Isocehedral Degree 5 Type I Geodesic Origami - In HandUnfortunately, the Applied Synergetics site (home of the DOME software) appears to have gone offline and is now being occupied by a squatter. Various repositories keep the package alive, as a bit of digging with Google will reveal. C. J. Fearnley has more about geodesic spheres in his excellent Buckminster Fuller FAQ.

Higher-quality images will follow at a later date; these were taken using a camera phone of inferior resolution.

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I’ve been rereading R. Buckminster Fuller’s Synergetics thanks to a Christmas gift. Thus primed, I was amused to come across two tetrahedron-related posts on BoingBoing:

Bucky was, of course, fascinated by tetrahedra:

113.00 When we take two triangles and add one to the other to make the tetrahedron, we find that one plus one equals four. This is not just a geometrical trick; it is really the same principle that chemistry is using inasmuch as the tetrahedra represent the way that atoms cohere. Thus we discover synergy to be operative in a very important way in chemistry and in all the composition of the Universe. Universe as a whole is behaving in a way that is completely unpredicted by the behavior of any of its parts. Synergy reveals a grand strategy of dealing with the whole instead of the tactics of our conventional educational system, which starts with parts and elements, adding them together locally without really understanding the whole.

(From the online text of Synergetics.)

For more tetrahedral goodness, check out these instructions for making a model of five interlocking tetrahedra from Thomas Hull. I’ve made several of these, and they’re great fun (on the most recent, the tolerances were a bit off, so it ended up being four interlocking tetrahedra). Here’s a nice image of a completed model.

If you’re not up to modular origami, you can also try this printable PDF papercraft version of five tetrahedra as a compound solid.