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Antiparallel strong traces (ASTs) are a type of walks in graphs which use every edge exactly twice. They correspond to 1-face embeddings in orientable surfaces and can be used to design selfassembling protein or DNA strands. Based on a novel canonical form invariant for ASTs, gap vector, we provide a linear-time isomorphism test for ASTs and thus, also for orientable 1-face embeddings of graphs. Using the canonical form, we develop an algorithm for enumerating all pairwise non-isomorphic 1-facedoi:10.1137/1.9781611975055.14 dblp:conf/alenex/HellmuthKKMN18 fatcat:qwse7gt4vjhkbf3hsfifdh3ruu