1:A=(-1.2208577248401677090604559983157963834, -3.1468480523080114886881271169977579250)
2:B=(-1.9478233124221029597568335446233091471, -1.9030657422906829627855358303024612249)
3:C=(-2.7527647907411112446780188831961624579, -3.5363463784316339145936381145450808675)
4:D=(-0.82783248947524419914841475107311902588, -0.80881034795529151745796572847987162035)
5:E=(0.73831734921240420520581932243142318234, 1.9030657422906829627855358303024612258)
6:F=(1,0)
7:G=(-1.8691742383633934665857228826763170467, 0)
8:H=(-1.5323609202837326010799277620171050618, -1.6348501262607572224466639246140796226)
9:I=(-1.9854399388298223415753940842379802469, -2.8132724283050665407238088353110992720)
10:J=(-2.2258288971159533487712352984471172569, -1.4274195298222514843054347812245927651)
11:K=(1.3430703308172535824813264335273661652, -2.4949510095897986824206185955346039503)
12:L=(-0.52723171215234560757205083333012202590, 0.97941058062225676502940186295657279032)
13:M=(0,0)
14:N=infinty

4 consecutive letters forms a circle, such as circle ABEG,ABHI, etc
ABEGABHIABJNABKMACDGACEFACHJACKNACLMADHKADIJADLNAEHLAEIKAEMNAFHMAFILAFJKAGHNAGIMAGJLBCDFBCHKBCIJBCLNBDHLBDIKBDMNBEHMBEILBEJKBFHNBFIMBFJLBGINBGJMBGKLCDHMCDILCDJKCEHNCEIMCEJLCFINCFJMCFKLCGHICGJNCGKMDEFGDEINDEJMDEKLDFHIDFJNDFKMDGHJDGKNDGLMEFHJEFKNEFLMEGHKEGIJEGLNFGHLFGIKFGMNHILNHJKNHJLMIJKMKLMN

Singular file to find the solution:
https://github.com/emathgroup/selectedTopics/blob/master/content/attached/files/KLM.sp
Output of the Singular file
https://github.com/emathgroup/selectedTopics/blob/master/content/attached/files/KLM.sp.out