Figure 5.

Development of the elevation diagram of the green DAD edge of hex-Ring 611. (A) With the four points 1, 2, 3, and 4 in this configuration, the dihedral angle between two planes 123 and 234 gives the angle of rotation of far (thin) edge 34 from near (thick) edge 12 about their common edge 23. Far edge 34 and near edge 12 are part of the central face and are thus internal edges. The angle through which far internal edge 34 is rotated from near internal edge 12 (about their common edge 23), the internal rotation about edge 23, is equal to the dihedral angle between the 123 and the 234 planes. Far edge 35 and near edge 26 are part of a surrounding face and are thus external edges. The angle through which far external edge 35 is rotated from near external edge 26, the external rotation about edge 23, is equal to the dihedral angle between the 623 and 235 planes. (B) Rotating the Ring in part A clockwise and then tilting the top of the Ring backward makes common edge 23 appear shorter. The near internal edge 21 and the near external edge 26 are thick, and the far internal edge 34 and the far external edge 35 are thin. (C) An enlargement of part of B. (D) Tilting the top of C farther backward shortens edge 23 even more, making it appear as a point and making the four planes appear as lines. In this elevation diagram, the change in dihedral angle of internal edges 34 from 12 provides the internal rotation I, and the change in dihedral angle of external edges 35 from 26 provides the external rotation E.