16 Triangles
Extract from MindBlowing Modular Origami • By Byriah Loper • Published by Tuttle PublishingAbout
Modular Origami
I chose this model to be the first in the Wire Frame section because it is relatively easy, though it appears complicated. When I first designed it, I set out to make an eighttriangle compound by combining two different compounds of four triangles that each had tetrahedral symmetry. When I finished, I realized more triangles could be added, and thus increased the model from eight to sixteen triangles. This model has the fewest units of any Wire Frame in this book. It is also the only octahedral symmetry model in the book.
The paper proportions are 1:4. Ripping the paper from 6" squares makes a ~7" model.
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You Will Need

Step 14
Weaving Instructions
The first four frames will be the basic structure on which additional frames can be added. This set of four frames has tetrahedral symmetry. The upper right photo shows the twofold symmetry, while the upper left shows the threefold symmetry. Each triangle represents one face of a tetrahedron. It will be unstable at this point, so frame holders can be used as shown. Note where a threefold axis appears in the picture on the left. 
Step 15
There will be four of those as well, following the vertices of a tetrahedron. The twofold axes, three of which are annotated on the right, will appear six times, aligning with the edges of a tetrahedron. By determining the symmetry of the shape, and its axes, you can begin to “intuit” the weaving in less visible areas, which will prove essential in many of the more complicated models presented later on in this volume.

Step 17
Note that each triangle has the same inandout weaving relationship with every other triangle except its opposite on the threefold axis. An example of one such pair is the yellow and dark blue, as circled in the lower right picture on the opposite page. These two have the relationship shown in the below left diagram with every other triangle except each other. As the symmetry of the shape becomes apparent, you should be able to guess where the three and fourfold axes are on the other side of the model, using the octahedra below for guidance.

Step 18
Adding the next set of four triangles, as shown in the images, requires a slightly greater understanding to weave correctly. At this point, the model has octahedral plus tetrahedral symmetry. Again, the set of four triangles is tetrahedral, and has four threefold axes, which represent the vertices of a tetrahedron.

Step 21
Assembling the last four triangles is probably the easiest part of the weaving process. The previous four triangles represented a tetrahedron poking through four faces of an octahedron; the remaining four represent another tetrahedron which will fill the remaining four threefold axes, as shown on the bottom left.