Cube

This structure contains 8 vertices and 12 edges. Since the cube is three-regular, augmenting edges must be added so that all the vertices are of even degree and threading can occur.* These augmenting edges are represented by the light blue lines in the first figure below; the dark blue lines represent the original edges. The figure to its right illustrates with different colors the 4-way rotational symmetry around the central square face that can be achieved as a result.

*This will be the case for all of the polyhedra in this project, since they are all three-regular.

With this placement of the augmenting edges, there is only one vertex arm type. Using the symmetrical rotation from above, we found the Euler circuit for the cube shown below. The black arrows indicate the direction of the scaffolding strand.

Threading sequence: 1, 6, 7, 1, 2, 7, 8, 2, 3, 8, 5, 3, 4, 5, 6, 4, 1

Once the threading and stapling are included, 2 unique vertex configurations are produced. The directions of both the scaffolding strand (black) and the staple strand (red) are indicated in this closer look at the different configurations.