Abstract
In this chapter, based mainly on [DeDu04], we focus on generalization of zigzags for higher dimension. Inspired by Coxeter’s notion of Petrie polygon for \(d\)-polytopes (see [Cox73]), we generalize the notion of zigzag circuits on complexes and compute the zigzag structure for several interesting families of \(d\)-polytopes, including semiregular, regular-faced, Wythoff Archimedean ones, Conway’s \(4\)-polytopes, half-cubes, and folded cubes.
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Deza, MM., Dutour Sikirić, M., Shtogrin, M.I. (2015). Zigzags of Polytopes and Complexes. In: Geometric Structure of Chemistry-Relevant Graphs. Forum for Interdisciplinary Mathematics, vol 1. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2449-5_8
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DOI: https://doi.org/10.1007/978-81-322-2449-5_8
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