By introducing antisextet dualists of sextet-resonant benzenoids that have only "full" and "empty" rings as defined by Clar, it was possible to devise a simple algorithm for an exhaustive enumeration of such sextet-resonant benzenoids (SRBs). Several relationships between invariants of such SRBs are described. All possible SRBs with up to 10 sextet rings are enumerated. A unique coding of SRBs is presented, based on the peripheral "sextet-polyphenyl-necklace" formed by the benzenoid rings circumscribing the SRB.