300 REV. T. P. KIRKMAN ON THE ENUMERATION, DESCRIPTION, AND 



in c4h, (ch) = 53,44>(32) = 53, 44 ? (67) is 43 ; 

 (/c)=44 >(76) = 43; 

 (dh) =U >(76or32) = 43; 

 (gg) = 44, 44 > (76 or 32) = 44, 43 

 (eg) =43, 53 > (76) = 43, 53? 

 (ei) =43, 43 > (76) =43,43? 

 (hi) =43, 54>43, 43 ; (23) is fixed (art. 23). 

 For the rest, 



(32) leads del, gi, ci, and 7tc=43. 



We have twelve flaps to draw, expecting with three at least symmetry 



(fd) gives 9 P ; 



(fc) 



gives 9 V ; 



(ffl n 9 Q; 



(dh) 



n 9 " J 



(cd) „ 9 R ; 



(oa) 



x- 



^i) » 9 s ; 



(^) 



Y- 



» 9 1 3 



(ch) „ 9 T; 



(ei) 



» 9^; 



(dg 7 ) „ 9 U ; 



(hi) 



„ 9 A«. 



The poles of 9 X are a tessarace and the leading flap. The symmetry and 

 circles of all are read on figures. 



51. Our next subsolid base is E 7 appended, on which no two edges are 



alike. Thirty-one different flap-lines can be drawn 

 4 on it, namely, 



hd, hf, cd, cc,fe, all 63 ; 



he, be, cf, fd, de, all 54 ; 



ae, ah, Im, Ij, hm, hj, hi, ie, all 53 ; 



ai, hi, eh, jm, all 44 ; 



fm, nf nm, gk, gi, ik,jd,jJc, Jed, all 43 ; 



the lines Im, &c, in the base being supposed dotted. 



(hf) =63, 43 > (67)= 63, 43 ? 54=44 ; 

 (cd) =63 >(54)=43; 

 (ee) =63 >(54) = 53; 

 (be) =54 >(54)=43; 

 (k) =54 >(54or67) = 53; 

 (cf) =54, 43>(23)=54, 43? (54)=44; 

 (/d)=54 >(23 or 54) =44 and >(67)=53; 

 (de) =54 > (54) = 53, or (67) = 43 ; (23) is fixed ; 

 (Im) = 53, 43 > (67) = 53, 43? (67) =44; 

 (dh) = 43, 64 > (54) = 43, 64 ? (67) and (23) are fixed 

 (ie) =53, 64 > (54) = 53, 64? 



For the rest, 



(23) leads nf, ah, ae, ai, mh, ef wj, mn ; 

 (67) „ hl,he,hi,bd,lj,jd,mf; 

 (54) „ gi,gh,ilc,jk,jh. 



