Figure 1

Rewiring sites of different dimer structures. (a)–(c) Theta structure and two chiral omega structures (simulations by Ravnik [7]). Rewiring sites are marked and paired with corresponding idealized structures. (d) The three conformations of a disclination crossing with tetrahedral symmetry. Rewiring is performed by rotating around a $C_3$ symmetry axis of the tetrahedron.Reuse & Permissions

Figure 2

To describe a disclination line, we introduce a ribbon, defined by an axis curve and a secondary curve that follows the orientation of the field cross section of the disclination. The ribbon may reconnect with itself with an offset angle of $\pm 120°$ while keeping the director field continuous, due to the symmetry of its cross section.Reuse & Permissions

Figure 3

(a) Tetrahedral rotation changes the positions of two disclination line segments, which also changes the curve, traced by the tangent on the unit sphere. The spherical area traced by this curve changes by $\pm 4\pi /6$ (shown in red), which is directly related to the $\pm 2/3$ change in writhe and consequently, the self-linking number. (b) Schematic depiction of dimer structures and transformations between them. A tetrahedral rotation changes the writhe by $\pm 2/3$ if parametrizations of initial and final structure are the same. By varying the parametrization, we can calculate writhes of all different dimer structures. Depicted here are the theta, chiral omega, and figure-eight structures and the pair of Saturn rings, with their respective self-linking numbers. Structures that consist of two loops are shown with both possible choices of parametrization. Orientations of loop parametrizations are indicated by arrows.Reuse & Permissions