There are 35 free polyominos with 6 cells

18 of them are path-coverable

17 of them are coil-coverable

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Table for 6

nameblankpath solutionspath solution imagescoil solutionscoil solution images
107374182322
161061273522
187904819100
201326591900
348966092743
362387865500
369098751922
374970777522
389231411120
402233753500
419430399922
765041049516
12
777623961500
778043391921
785173708722
791045734322
812017254300
830891622300
831723929500
835505356722
838651084700
838755942322
845257113522
1623615078300
1623824793543
1670591283100
1670800998300
1670905855922
1676463308700
1677295615900
1677407027122
1690507673500
1690714111922
5052878028700
5053087743900