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Structural possibilities are considered for what arguably is the most general class of connected "pure-polyhex" π-networks (of carbon atoms). These are viewed as hexagonal-network coverings (i.e., a tiling by hexagons) of a connected locally Euclidean surface S possibly with holes which can be simple cycles of sizes other than 6. The surface S can curve around to connect to itself in different ways, e.g., with handles of different sorts. This then includes ordinary benzenoids, coronoids, carbondoi:10.5562/cca3790 fatcat:e2svrumekva7vk5puqnj3yryn4