Truncated Cube

To obtain the truncated cube, the corners of a cube are "sliced off," creating equilateral triangles where the corners were and transforming the square faces of the cube into regular octagonal faces. The final structure has 24 vertices and 36 edges. The figure below is a Schlegel diagram of a truncated cube, projected through the triangular center face. There are two augmenting edges (light blue) added in each octagonal face of the complex. The black arrows indicated the direction of the scaffolding strand that forms an Euler circuit during threading.

Threading sequence: 1, 2, 5, 18, 19, 20, 21, 22, 23, 10, 8, 7, 21, 19, 7, 6, 2, 3, 6, 8, 9, 10, 11, 23, 24, 15, 13, 12, 11, 9, 12, 4, 3, 1, 4, 13, 14, 15, 16, 24, 22, 20, 18, 17, 16, 14, 17, 5, 1

With the 3-way symmetry that this circuit yields, there are only 3 unique vertex configurations necessary for self-assembly of the truncated cube. The diagram of these configurations shown below includes the directions of both the scaffolding strand (black) and the staple strands (red).