Symmetry is an intriguing phenomenon manifesting itself in art, nature, and the mind. This Special Issue book features 19 articles about discrete geometric and combinatorial polyhedral structures, with symmetry as the unifying theme. These articles present an attractive mix of topics and have appeared in two related Special Issues of Symmetry, on "Polyhedra" in 2012/2013 and on "Polyhedral Structures" in 2016/2017. Specific topic areas covered include polyhedra, tilings, and crystallography; abstract polyhedra, maps on surfaces, and graphs; and polyhedral structures, arts, and architectural design.

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