Swallowtail Module (Dog Bone Unit)

Model details: Swallowtail Module (by: Jennifer Campbell, Michał Kosmulski)
See also: Cube

Model types: single unit
Location: on this page, on other website
Type: Phototutorial

This is a business card unit which I designed independently with Jennifer Campbell who used the name Dog Bone Unit (details in model description).

Instructions on the web

You can find her instructions on this web page.


Folding a unit

Step 1
1. Start with a business card or a sheet of stiffer-than-usual, rectangular piece of paper.
Step 2
2. Valley fold in half along the longer axis.
Step 3
3. Crease at a 45° angle, but only up to the crease created in previous step.
Step 4
4. Crease as in step 3 in the other corner.
Step 5
5. Repeat the creases from steps 3-4 on the other side. You should now have 4 symmetric creases at 45° angles originating in the four corners of the card.
Step 6
6. Squash fold using the creases created in previous steps. The module is ready. In this picture it is seen from the bottom.
Step 7
7. Finished Swallowtail module seen from the side.

Assembling a cube from units

Swallowtail units can be used to fold a cube. I believe that with units made from somewhat slimmer modules (paper with 3:1 ratio or similar), one could fold the units in half and create some spiky balls based on triangular spikes (similar to this spiked dodecahedron), but haven’t yet tried it in practice. In either case, at any vertex three units are connected to each other. The “swallow’s tail” of each unit is interwoven with the corresponding part of the other two units, creating a small sunken pyramid at the vertex. This connection is quite stable once all units are connected (since the different forces cancel each other out) but a little fragile as long as the whole polyhedron is not yet complete. The joint works due to the business card’s high stiffness. A similar connection made of regular paper wouldn’t hold. Some units made from regular paper, most notably the PHiZZ module, use a similar connecting structure, but they need an additional sheet of paper in the pyramid while in the business card version one layer less is enough.

Step 8
8. Three modules connected together show the connecting mechanism. Note the inverted pyramid structure. It can be seen from the other side in the picture of the finished cube below.
Step 9 — finished cube
9. With all twelve edges added, the cube is ready. Note the inverted pyramids at each vertex.