Figure 6.

Internal and external rotations in the models of probable Ring 611 and Ring 623 composed of aluminum atoms. (A) In this view, the model of hex-Ring 611 from aluminum atoms appears as an upwardly curving bowl. The pentagon is at the back and rises above the floor, and two green DAD edges emerge from it. With reference to the a and a′ edges, nearly on the floor of the bowl, the b and b′ edges rise, and the c and c′ edges rise even more. (B) The central face in this aluminum model of Ring 611 has two Sym edges (S and S′) that cross the line of mirror symmetry. Each mirror-symmetric half also has a green DAD edge (G or G′) and a Twist edge (T or T′). Each of the central edges has an elevation diagram in its surrounding face. In each elevation diagram, the internal edges are shown on the left, the external edges on the right. This convention follows from looking end-on down each central edge from the point of view of its associated arrowhead. As in Fig. 5 D, a clockwise rotation from a front (thick) edge to a back (thin) edge is positive. The central edges are labeled S, G, and T—Sym, Green, and Twist—for the right side of the Ring and S′, G′, and T′ for the left side. The external edges are labeled a, b, and c for the right side of the Ring and a′, b′, and c′ for the left side. (C) Hex-Ring 623, here shown as an upwardly curving bowl, has four green DAD edges. (D) The elevation diagrams for Ring 623 follow the description in part B, except that the labeling of central edges (G, G′, G″, $G^{‴}$) and of external edges (a, a′, a″, $a^{‴}$) takes advantage of the two mirror-symmetric axes between left and right halves and between top and bottom halves.