CONSTRUCTION OF KNOTS OF FEWER THAN TEN CROSSINGS. 295 



For the rest, 



(56) leads (fa) and (fb) from the flap (12), 



and (12) leads (?>&)= 43. 



We have to draw five flaps, presuming symmetry with (ba), (bb), and (ff). 



(ff) g iv es us 8 H, 



whose three 2-zoned janal axes terminate in the centres of the zoned polar 

 flaps and of two pairs of edges 44, 44 ; and 33, 33. 



(Kb) gives us 8 I, asymmetric, 

 (bb) gives us 8 J, 



whose two janal zoned poles are 4-gons, the four like janal zoneless 2-ple poles 

 being edges 44. We often mean by pole the polar face summit or edge in 



wh'ich an axis ends. 



(act) gives us 8 K, 



having two different zoned polar flaps : 



(ba) gives us 8 L,. 



whose zoneless poles are 44 and 55. 



43. Our next base is 6 C, which has one flap, one triangle, and one 4-gon. 

 The only different lines that can be drawn are ff and aa, 

 each 44, and /a and aa, each 43. The two/'s are alike. 



(ff) =44, 33 > (23) =43, 33? 



(aa) = 44 >(32) or (56) or (14) ? each =44; 

 not (/«)=53 >(14)=5i; 

 nor (aa)=43 >(14) = 54. 



We have two flaps only to draw. 



(ff) gives 8 M, 



whose zoned poles are the flaps, the four like zoneless 2-ple poles being 



tessaraces. 



(aa)—A.A gives 8 N, 



whose eight janal secondary 2-zoned poles are alternately flaps and 4-gons. 



44. We have no more subsolids of six crossings. Of the unsolids, we 

 find only four, 6 D, 6 E, 6 F, and 6 G, on which a flap can be drawn to block linear 

 section. 



We have on 6 D, in \aa, and 14««, 



(aa)=53>(34) and >(56), each =43. 

 (aa)=44>(34) or (56) each=43. 



By (aa)=53 we get 8 P. 



By (aa)=44 we get 8 Q, vide the figures. 



