Abstract
: This mini review concerns hydrocarbons, (CH)n, and carbon allotropes, Cn, and their relationships with regular solids and regular surfaces, respectively. Platonic and Archimedean solids and surfaces related to carbon allotropes are described as an introduction. An overview is then provided on how Stone-Wales defects lead to a series of structures: pentaheptite, Haeckelite, net C, net W, planar C4, biphenylene, graphyne, graphdiyne, and tetraoctite. This last compound is discussed in detail together with its relation to the Mills-Nixon effect on cyclooctatetraene (COT).
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