Cirroteuthis muelleri, also known as the big-finned jellyhead, was the first cirrate octopus species (and genus) to be scientifically described (in 1836). It is closely related to the genus Cirrothauma within the family Cirroteuthidae. The species is restricted to the Arctic Ocean and far North Atlantic (specimens from the southern hemisphere and Pacific have been attributed to a new species Cirroteuthis kirrilyae Verhoeff & O'Shea, 2025).

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