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We present a fully automatic method for complete analysis of planar ornaments in $13$ of these groups, specifically, the groups called $p6m, \\, p6, \\, p4g, \\,p4m, \\,p4, \\, p31m, \\,p3m, \\, p3, \\, cmm, \\, pgg, \\, pg, \\, p2$ and $p1$. 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