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We consider the efficient computation of sequences of push actions that simultaneously orient two different polygons. Our motivation for studying this problem comes from the observation that appropriately oriented parts admit simple sensorless sorting. We study the sorting of two polygonal parts by first putting them in properly selected orientations. We give an O(n 2 log n)-time algorithm to enumerate all pairs of orientations for the two parts that can be realized by a sequence of pushdoi:10.15607/rss.2005.i.013 dblp:conf/rss/BergGS05 fatcat:wjixetaxmrbyjnocxeizyiawha