Chirality is one of the basic characteristics of biological structures; chirality is a symmetry property. Multi-tori are complex structures consisting of more than one torus, embedded in negatively curved surfaces. Design of multi-tori may be achieved by operations on maps. The “monomers” used to design the chiral multi-tori discussed in this chapter are snubs of Platonic solids. A snub polyhedron s(P) is achieved by dualizing the p5(P) transform: s(P) = d(p5(P)); since p5-operation is prochiral, all the consecutive structures will be chiral; high genus structures of rank k = 3 were thus obtained. The genus and rank (or space dimension) of a structure are parameters of complexity.
Topological symmetry of the structures herein discussed was evaluated by ring signature and centrality index and confirmed by symmetry calculation using the adjacency matrix permutations. C60-related chiral tori were also designed and their symmetry evaluated. An atlas section illustrates the discussed chiral multi-tori.
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