How to Make Modular Origami (Very Cool Design in 2022)

The first four frames form the basic structure, to which further frames can be added. This set of four frames has a tetrahedral symmetry. The top right image shows a twofold symmetry and the top left image shows a threefold symmetry. Each triangle represents a facet of a tetrahedron. At this point it will be unstable, so the frame holders can be used as shown. Notice where the triangular axis appears on the left side of the diagram.

There will also be four of them following the vertices of the tetrahedron. The bilateral axes, three of which are marked on the right, appear six times and coincide with the faces of the tetrahedron. By recognizing the symmetry of the shape and its axes, you can begin to “intuitively understand” the mesh in less visible areas, which will prove important in many of the more complex patterns presented later in this volume.

Above are eight images. Each triangle now represents a facet of an octahedron. There are six tetrahedral axes, as shown above on the left, and eight tetrahedral axes, as shown above on the right. Note that each triangle has the same interlacing relationship with every other triangle except the opposite triangle on the triple axis.

An example of one of these pairs is yellow and blue, as circled on the opposite side in the figure below right. These two triangles have the relationship shown in the figure below on the left to all other triangles except each other. As the symmetry of the shape becomes obvious, you should be able to guess where the three- and four-sided axes are on the other side of the model, using the octahedra below as a guide.

Requires a little more understanding of the correct weaving. At this stage, the pattern has the symmetry of an octahedron plus a tetrahedron. Again, the set of four triangles is tetrahedral and has four tetrahedral axes representing the vertices of the tetrahedron. New tetrahedral axes must lie within four of the eight existing tetrahedral axes.

The circled frames are the new frames, the right image shows one of the new triangle axes, and the left image is a view from the exact opposite triangle axis. Although this step can be confusing at first, the model should now be relatively stable if assembled correctly, and it will be easier to work with.

The previous four triangles were a tetrahedron that pierces the four faces of the octahedron; the remaining four are another tetrahedron that will fill in the remaining four triangle axes, as shown below left. There are four groups of four parallel triangles circled on the right.

If you have any doubts about the weaving, you can use this rule to check.

Then check to make sure everything is correct. If you see a kink or other distortion, a mistake has probably been made somewhere.

The diagram below is not strictly necessary; it is just to illustrate the basic geometric relationship.