of Edinburgh, Session 1885 — 86 . 
695 
The second knot has four 2-gons, fb, FB, Ge, gD. At fb 
. . afbD . . , . . C fbg . . are meshes collateral with it; and as &D and 
gD are edges, Dbg is a triangle collateral with . . C 'fbg . . which we 
choose for our base. The 2-gon gD is collateral with . . bgDa . . and 
. . DgDc . . . Since bg cannot be in three meshes, . . C fbg . . is 
. . bgDa . ., and our base is . . C fbgDa ... As DC and Da are edges, 
this base is the 7-gon DCfbgDa. Inside this, with d remote from 
D, c from C, &c., we have to draw the heptagon dcY BGeA, and we 
complete the projection by the edges af, AE, bD, B d, bg, BG, cE, 
Ce, cA, C a, and by making the 2-gons Ge, gD, fb, FB. There is a 
zonal trace across the epizonal edges bg and BG, and the mid-points 
of the identical zoneless polar edges ae and AC, are the poles of a 
zoneless 2-ple contrajanal axis, about which in revolution there is a 
2-ple repetition. We have constructed a 2-ple monaxine monozone 
subsolid knot. There are 2-ple monaxine monozone unsolid knots 
that have 12, 10, and 8 crossings only. 
The 12-filar knot of 180 crossings, whose circles under written 
completely define it, has a zoneless symmetry of the highest possible 
complexity, and is the simplest knot of that symmetry that can be 
formed. Required its meshes and its symmetry. 
abcaf 1 cdefm 2 n 2 fghijf 8 ij7da n b 11 lmnpaf 3 p , 
a^ 1 c 1 abc x d 1 ej 1 mp,j ! ggjifamp^ 
^&4 C 4i3 / % C A e 4/4i9^9/4^ /i 4 ? >6 & 6VV^ / 4 a 5 & 5^^4^4P4.^1 7 hP4 5 
a fb C bi)J C 4pb^b e bfb m 6 n Qfbdb^bH a ^Hjf‘bK < ^i e ^'b m b ri b'Pbj^'lPb » 
a 8^8 C 8^7^7 C 8 < ^8 e 8/8 m l0 7Z 'lo/85 r 8^'8 ? 'S^ll e 11^8^8^8^8^^8 m 8 W &? 9 S^2^2i ? 8 ’ 
%0^10 C 10#^7 C 10^10 e lo/l0^6^6/l0^10^10^10^9 e 9^10.?10^10^10^11^11^10 m lO%oP]0^8 e 8^1(P 
a il^ll C ll^^ C ll < ^li e ll/ll0 r 8^'8/ll^ll^llhl^lO^lohl^ll^ll^li a 9^9^1i m il ?? llPll^3 e 3i ? ll * 
Ho duad is found twice in the circles, except the pair of crossings 
of a 2-gon, which is read twice, as ab. Every crossing s occurs 
