SharedHnorm.ipynbOpen in CoCalc
Jupyter notebook Hnorm.ipynb
import numpy as np
from cvxopt import matrix, solvers
def Hnorm(A):
    # Regner ut Hilbert-norm til numpy matrise A
    rad, kol = A.shape
    nullr = np.zeros((rad,rad))
    nullk = np.zeros((kol,kol))
    C = np.bmat([[nullr,A],[A.T,nullk]])

    h0 = [ -0.5*matrix(C) ]

    dim = rad+kol
    c = matrix(np.ones(dim,))
    # Vil lage diagonalmatriser A_i med 1 på plass (i,i), 0 ellers
    diagonal = np.zeros(dim,)
    diagonal[0] = 1
    A0 = np.diag(diagonal)
    G = A0
    for i in xrange(1,dim):
        A0 = np.diag(np.roll(diagonal,i))
        G = np.bmat([[G],[A0]])
    # G0 er nå blokk matrise med A_i'ene stabla nedover i radene.
    G0 = [ matrix(-1.0*G) ]
    solvers.options['show_progress']=False
    solvers.options['abstol'] = 1e-11
    solvers.options['reltol'] = 1e-10
    sol = solvers.sdp(c, Gs=G0, hs=h0)
    norm = -1
    if sol['status'] == 'optimal':
        norm = sol['primal objective']
    return norm

def ekstrem_ell_infty_recursive(N):
    ekstrem_punkt = np.zeros((2**(N-1),N),dtype=np.int)
    if N == 1:
        ekstrem_punkt[0] = 1
    else:
        ekstrem_punkt[:,0] = np.ones((2**(N-1),),dtype=np.int)
        E = ekstrem_ell_infty_recursive(N-1)
        ekstrem_punkt[:2**(N-2),1:] = E.copy()
        ekstrem_punkt[2**(N-2):,1:] = -1*E.copy()   
    return ekstrem_punkt
    
def ekstrem_ell_infty2(N):
    return ekstrem_ell_infty_recursive(N).transpose()

def Mnorm(A):
    # Regn ut norm max(|Ax|_1, x kolonne i E)
    rad, kol = A.shape
    E = ekstrem_ell_infty2(kol)

    # Ta absolutt verdi av elementene og summer kolonnevis
    return np.max(np.sum(np.abs(A*E),axis=0))
    # Eventuelt 
    # return reduce(max,np.sum(np.abs(A*E),axis=0))

def finnKG(matrise):
    """Tar ei matrise på formen '{{1,1},{1,-1}}' (en streng)
    og returnerer Mnorm, Hnorm og forholdet Hnorm/Mnorm"""
    M = matrise
    M = M.replace('},{',';')
    M = M.replace('{{','[')
    M = M.replace('}}',']')
    M = np.mat(M)
    norm_M = Mnorm(M)
    norm_H = Hnorm(M)
    KG = norm_H/norm_M
    return (norm_M, norm_H, KG)

be1='{{-1,0,0,0,-1,0,1,1},{1,1,0,0,0,-1,1,0},{-1,1,0,1,0,1,0,0},{1,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,0},{0,0,-1,0,1,0,1,1},{-1,0,0,0,0,1,1,-1},{1,0,1,1,0,0,0,1}}'

be2='{{0,2,1,1,-1,0,1,0},{-1,1,0,0,1,-1,0,0},{0,0,0,0,0,0,0,0},{0,1,0,-1,1,0,-1,0},{0,0,0,0,1,0,1,0},{0,0,0,0,0,0,0,0},{0,0,0,1,1,1,1,0},{1,0,1,1,1,0,-2,0}}'

be3='{{-1,-1,0,0,1,0,0,1},{-1,1,0,0,0,0,0,0},{1,1,1,0,-1,0,1,1},{0,1,0,0,0,0,-1,0},{0,1,0,1,0,0,1,-1},{0,1,0,0,1,0,0,0},{0,0,0,0,1,0,1,0},{1,0,-1,1,0,0,0,1}}'

be4='{{-1,-1,1,1,0,0,0,0},{-1,1,0,0,0,0,0,0},{1,1,-1,0,0,0,1,0},{0,1,1,0,0,1,1,0},{0,1,1,1,0,-1,0,0},{1,0,1,0,0,0,0,0},{0,0,-1,2,0,0,1,0},{0,1,0,0,0,0,-1,0}}'

be5='{{0,0,1,1,1,-1,1,1},{-1,0,1,-1,1,0,1,1},{0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,1},{-1,0,1,0,0,0,-1,1},{0,0,-1,0,0,0,0,1},{0,0,1,0,-1,0,1,-1},{1,0,1,0,1,1,0,0}}'

be6='{{0,0,1,-1,1,0,0,1},{-1,1,0,0,1,0,0,1},{0,1,0,1,-1,0,0,1},{1,1,-1,-1,1,0,1,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,1},{0,0,0,1,1,0,1,-1},{0,1,0,0,1,0,-1,-1}}'

be7='{{-1,0,-1,1,0,0,0,1},{-1,1,0,0,0,0,0,0},{0,1,0,-1,0,0,0,0},{0,1,1,1,0,-1,1,1},{1,1,0,1,0,1,0,0},{1,1,0,0,0,0,1,1},{0,-1,0,0,0,0,1,0},{0,0,0,0,0,0,1,-1}}'

be8='{{-1,0,0,0,1,0,0,0},{-1,1,0,0,0,0,0,0},{1,0,-1,1,0,0,0,1},{0,1,0,1,1,0,0,1},{0,1,1,0,-1,0,0,1},{0,0,0,0,0,0,0,0},{0,-1,1,1,0,0,1,0},{1,0,1,1,1,0,-1,-1}}'

be9='{{1,-1,0,0,0,1,0,1},{-1,1,0,0,1,1,1,1},{1,0,0,0,1,1,1,0},{1,1,0,0,1,0,0,-1},{0,-1,0,0,1,0,0,0},{0,0,0,0,1,-1,0,0},{0,0,0,0,-1,0,2,-1},{0,0,0,0,0,0,0,0}}'

be10='{{-1,0,0,0,0,0,0,1},{-1,0,0,0,1,0,1,1},{0,0,0,0,0,-1,1,0},{2,1,1,0,0,1,2,1},{1,0,-1,0,0,1,0,1},{0,0,0,0,0,0,0,0},{-1,0,0,0,0,1,1,-1},{0,1,0,0,1,0,-1,-1}}'

be11='{{0,-1,0,1,0,0,0,0},{-1,1,0,0,0,0,0,0},{0,0,-1,0,0,1,0,0},{1,1,1,1,0,0,-1,1},{-1,0,1,1,0,1,1,1},{0,0,0,0,0,0,0,0},{1,0,0,0,0,1,0,0},{0,1,1,1,0,1,0,-2}}'

be12='{{-1,-1,1,0,0,1,0,0},{0,1,1,1,0,-1,0,0},{0,0,0,0,0,0,0,0},{0,0,1,0,0,1,0,0},{0,1,1,-1,0,0,0,1},{1,1,0,-1,0,1,0,0},{1,0,0,0,0,1,-1,-1},{1,0,0,1,0,1,1,0}}'

be13='{{0,-1,1,0,-1,0,0,1},{-1,0,0,1,1,0,-1,0},{-1,-1,1,1,1,0,1,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{1,1,0,1,0,0,0,1},{0,0,-1,1,0,0,1,1},{1,1,1,0,1,0,1,-1}}'

be14='{{0,0,0,-1,1,0,0,0},{0,0,0,1,0,-1,0,0},{0,1,0,0,1,0,0,0},{0,-1,0,0,0,1,0,0},{0,1,1,0,-1,1,0,0},{1,-1,1,1,1,-1,0,0},{1,1,0,0,0,1,1,0},{0,1,0,1,0,1,-1,0}}'

be15='{{0,0,1,1,0,0,1,1},{0,1,0,0,0,0,0,-1},{0,0,-1,1,1,-1,0,0},{0,1,-1,0,2,1,0,1},{0,0,1,0,2,0,-1,0},{0,0,0,0,0,0,0,0},{0,1,0,0,0,0,1,0},{0,-1,0,0,1,0,1,-1}}'

be16='{{0,0,0,0,0,1,0,1},{-1,1,0,0,0,0,1,-1},{0,1,1,1,0,0,0,1},{0,0,-1,1,0,0,1,1},{-1,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,0},{1,0,0,0,0,1,1,-1},{1,0,0,2,0,1,-1,-1}}'

be17='{{-1,-1,1,-1,0,0,1,1},{0,1,0,0,0,0,1,0},{0,-1,0,1,0,1,0,1},{1,1,-1,0,0,1,0,0},{0,0,0,1,0,0,1,0},{0,0,0,0,0,0,0,0},{-1,1,0,0,0,0,0,0},{1,1,2,1,0,0,-1,0}}'

be18='{{0,1,0,1,0,0,0,0},{-1,1,-1,0,0,0,1,0},{0,1,1,-1,0,0,0,1},{1,1,0,0,0,1,1,0},{0,0,1,0,0,0,1,0},{0,0,0,1,0,-1,1,1},{0,0,0,0,0,0,1,-1},{0,0,1,1,0,0,-1,-1}}'

be19='{{-1,0,0,1,-1,0,0,1},{1,1,0,0,0,0,-1,1},{0,0,0,1,1,0,1,-1},{0,1,0,0,0,1,1,1},{-1,1,0,0,1,-1,1,1},{0,0,0,0,0,0,0,0},{0,0,0,0,-1,0,1,0},{1,1,0,0,0,0,1,-1}}'

be20='{{0,0,-1,0,0,0,1,0},{-1,2,0,0,0,0,1,0},{1,-1,0,0,0,0,0,2},{0,0,0,0,0,0,0,0},{1,1,1,-1,0,0,0,0},{-1,0,1,0,0,0,1,1},{1,-1,0,0,0,0,1,-1},{1,1,1,1,0,0,0,0}}'

be21='{{0,0,0,0,1,0,1,0},{-1,1,0,-1,1,1,-1,0},{0,0,0,0,0,0,0,0},{1,1,-1,1,0,1,1,0},{1,0,1,1,1,0,-2,0},{0,1,1,0,0,0,0,0},{1,0,1,-1,0,0,1,0},{0,-1,0,0,1,0,0,0}}'

be22='{{-1,-1,1,1,0,0,0,0},{-1,1,0,1,0,0,1,0},{0,0,0,0,0,0,0,0},{0,0,1,0,0,-1,0,0},{0,0,0,0,0,1,1,0},{0,1,1,0,0,0,0,0},{1,0,1,1,1,1,-1,0},{1,1,0,1,-1,1,-1,0}}'
map(finnKG,[be1,be2,be3,be4,be5,be6,be7,be8,be9,be10,be11,be12,be13,be14,be15,be16,be17,be18,be19,be20,be21,be22])
[(12, 16.750227725189358, 1.3958523104324465), (12, 16.201653428353676, 1.3501377856961396), (12, 16.82273487867139, 1.4018945732226158), (12, 16.31627002244219, 1.359689168536849), (12, 16.520807297019456, 1.376733941418288), (12, 16.617721980253172, 1.3848101650210978), (12, 16.83851703556276, 1.4032097529635632), (12, 16.19513065898604, 1.3495942215821701), (12, 16.113914776468352, 1.3428262313723627), (12, 16.59639994137973, 1.3830333284483107), (12, 16.13598837475396, 1.3446656978961633), (12, 16.44606570674319, 1.3705054755619326), (12, 16.53089732621919, 1.3775747771849325), (12, 16.766997954955993, 1.397249829579666), (12, 15.836609103664442, 1.31971742530537), (12, 16.0067665223266, 1.3338972101938833), (12, 16.70898114049221, 1.3924150950410175), (12, 16.79648424498621, 1.3997070204155175), (12, 16.753474992393677, 1.3961229160328064), (12, 16.13126357529154, 1.3442719646076284), (12, 16.105753707631266, 1.3421461423026055), (12, 16.570577645326836, 1.380881470443903)]
be1='{{0,0,0,0,0,0,0},{1,1,0,1,-1,0,0},{0,0,1,0,1,2,0},{1,0,1,0,0,0,0},{0,1,1,0,1,-1,0},{-1,1,0,0,0,0,0},{-1,-1,1,1,1,-1,0}}'

be2='{{0,0,1,-1,1,1,0},{0,1,0,-1,0,0,0},{0,-1,0,0,0,1,0},{0,1,0,1,1,0,-1},{0,1,-1,0,1,1,0},{0,1,0,0,-1,0,0},{0,1,0,1,0,1,1}}'

be3='{{-1,1,0,1,1,1,-1},{0,-1,0,-1,0,1,1},{1,0,1,0,1,0,1},{0,0,0,0,0,0,0},{1,1,0,0,0,0,0},{1,-1,-1,2,0,0,1},{0,0,0,0,0,0,0}}'

be4='{{-1,0,0,0,0,1,0},{0,-1,1,1,0,1,0},{-1,1,-1,0,0,1,0},{0,0,0,0,0,0,0},{1,1,1,-1,1,1,0},{0,0,-1,1,1,-1,0},{1,1,0,1,0,1,0}}'

be5='{{1,0,1,-1,0,0,1},{0,0,0,1,1,1,1},{0,0,1,1,0,0,0},{0,0,0,0,0,0,0},{0,0,-1,0,0,0,1},{-1,-1,1,0,-1,0,2},{0,1,0,1,0,-1,1}}'

be6='{{0,-1,0,0,1,1,-1},{1,1,-1,0,1,0,0},{0,0,0,0,0,0,0},{0,-1,0,0,0,0,1},{1,1,2,0,0,1,1},{1,0,-1,0,1,0,1},{1,0,0,0,-1,0,0}}'

be7='{{1,1,0,0,-1,0,1},{1,0,0,1,2,-1,1},{0,0,0,0,0,0,0},{-1,1,0,0,0,0,0},{0,0,0,-1,0,0,1},{0,-1,0,1,-1,0,1},{1,1,0,1,0,1,0}}'

be8='{{-1,1,0,0,-1,0,1},{1,1,0,0,0,0,0},{0,1,0,-1,0,0,0},{-1,1,0,1,2,0,1},{0,-1,0,0,0,0,1},{1,0,0,1,0,0,0},{0,1,0,1,-1,0,1}}'

be9='{{1,0,1,0,-1,1,0},{-1,0,0,1,0,0,0},{0,0,0,0,0,0,0},{0,-1,-1,0,1,1,0},{-1,1,1,-1,1,1,0},{0,-1,1,1,0,1,0},{1,1,0,1,1,0,0}}'

be10='{{0,1,0,-1,1,-1,0},{0,0,0,0,0,0,0},{1,1,0,-1,0,1,0},{-1,2,0,0,-1,0,0},{1,1,0,1,1,1,1},{0,1,0,1,1,0,-1},{-1,0,0,0,0,1,0}}'

be11='{{0,0,0,0,-1,1,0},{1,1,0,1,1,2,0},{0,0,0,0,0,0,0},{-1,-1,0,2,1,1,0},{1,0,1,2,-1,-1,0},{-1,0,1,-1,0,1,0},{0,0,0,0,0,0,0}}'

be12='{{1,0,1,-1,-1,0,0},{1,0,0,1,0,0,2},{0,0,0,-1,1,0,0},{0,0,1,-1,1,0,1},{-1,0,2,1,0,0,0},{0,0,0,0,0,0,0},{1,0,0,1,1,0,-1}}'

be13='{{1,-1,1,1,0,0,0},{0,1,-1,1,1,0,0},{0,0,1,0,1,0,0},{1,0,-1,0,-1,0,1},{0,-1,-1,0,1,0,1},{0,1,0,0,0,0,1},{0,0,1,0,0,0,1}}'

be14='{{0,0,0,0,0,0,0},{0,1,0,-1,0,0,0},{0,0,0,0,0,1,-1},{-1,0,0,1,0,1,1},{-1,1,0,1,0,0,-1},{1,1,1,1,0,1,1},{1,1,-1,2,0,-1,0}}'

be15='{{0,0,0,0,0,0,0},{0,1,1,1,1,-1,1},{0,1,0,1,0,1,1},{0,0,0,-1,1,0,0},{1,0,0,1,1,0,-1},{0,-1,0,0,0,0,1},{-1,1,-1,0,1,0,0}}'

be16='{{0,-1,0,1,0,1,-1},{0,1,1,1,1,1,-1},{0,0,-1,1,1,1,0},{0,0,0,-1,1,0,0},{0,0,0,0,1,0,1},{0,0,0,1,0,0,1},{0,0,0,1,0,-1,0}}'

be17='{{0,1,1,-1,0,1,0},{0,0,0,0,0,0,0},{1,1,0,1,1,0,0},{-1,0,1,-1,1,0,0},{1,-1,2,0,0,0,0},{1,-1,-1,0,0,1,0},{0,0,1,1,0,0,0}}'

be18='{{0,-1,2,0,1,0,0},{1,-1,0,0,1,1,0},{0,1,0,0,1,0,0},{2,1,1,0,-1,-1,0},{0,0,0,0,0,0,0},{0,0,0,0,-1,1,0},{1,0,-1,0,1,1,0}}'

be19='{{-1,0,0,-1,2,0,0},{1,1,0,0,0,1,-1},{1,-1,0,-1,0,0,1},{0,1,0,0,0,0,1},{0,-1,0,1,1,1,0},{0,0,0,0,0,0,0},{1,0,0,1,1,0,1}}'

be20='{{1,1,0,1,-1,0,0},{1,-1,0,0,1,1,0},{-1,-1,0,1,0,1,0},{0,0,0,0,0,0,0},{-1,1,0,0,0,0,0},{-1,0,0,1,1,-1,0},{1,2,0,1,1,1,0}}'

be21='{{0,0,0,0,0,0,0},{-1,1,0,0,0,0,0},{1,1,0,-1,0,1,0},{1,0,0,1,0,0,0},{1,0,-1,-1,0,0,1},{-1,-1,1,1,0,1,1},{1,1,2,0,0,0,0}}'

be22='{{0,1,1,1,0,1,0},{0,0,0,0,1,1,0},{0,1,-1,0,0,-1,1},{0,0,-1,1,1,0,1},{0,0,0,1,-1,0,0},{0,0,0,-1,-1,1,1},{0,0,1,0,0,0,1}}'

be23='{{0,1,1,0,0,-1,1},{1,0,1,-1,0,1,0},{0,1,0,0,0,1,0},{0,0,1,0,0,-1,0},{-1,-1,0,0,0,1,1},{1,0,1,1,0,1,0},{1,-1,0,0,0,0,0}}'

be24='{{-1,0,-1,0,1,1,0},{0,0,2,0,1,0,1},{-1,0,-1,0,1,0,1},{0,0,0,0,0,0,0},{1,0,0,0,0,0,1},{1,0,1,0,0,1,-1},{2,0,-1,0,1,0,0}}'

be25='{{1,1,-1,0,1,0,0},{1,0,0,1,0,0,0},{0,0,1,1,-1,0,1},{-1,-1,-1,1,1,0,1},{0,0,0,0,0,0,0},{0,1,0,1,0,0,0},{1,-1,1,0,1,0,0}}'

be26='{{0,0,0,0,0,0,0},{0,-1,0,1,1,0,-1},{1,0,0,0,0,1,0},{-1,0,0,1,-1,1,0},{1,0,0,1,0,0,0},{-1,0,1,1,1,1,1},{0,1,-1,0,1,1,0}}'

be27='{{-1,0,0,0,0,0,1},{0,0,0,0,1,0,-1},{0,-1,0,1,1,0,1},{1,1,0,0,1,0,1},{0,0,1,1,-1,0,-1},{1,0,1,0,1,0,1},{-1,0,0,0,1,0,0}}'

be28='{{1,0,1,0,0,0,0},{0,1,0,0,0,0,1},{1,-1,0,1,0,1,0},{0,1,1,0,0,1,-1},{1,-1,-1,-1,0,1,1},{0,0,1,0,0,0,1},{-1,0,0,0,0,1,0}}'

be29='{{0,0,0,-1,0,0,1},{0,0,0,0,0,0,0},{2,0,0,1,0,0,1},{0,-1,-1,0,2,0,0},{1,1,1,-1,1,0,-1},{-1,1,1,1,1,0,1},{0,-1,1,0,0,0,0}}'

be30='{{0,1,1,1,1,0,0},{-1,1,0,1,-1,0,0},{0,0,-1,0,1,0,0},{0,1,0,-1,0,0,0},{1,1,0,1,0,0,1},{0,0,1,1,1,0,-1},{0,0,-1,1,0,0,0}}'

be31='{{1,-1,0,0,-1,1,2},{0,0,0,0,0,0,0},{1,-1,1,0,1,-1,1},{0,0,0,0,1,1,0},{1,0,0,0,-1,1,-1},{1,1,1,0,0,0,-1},{0,1,0,0,0,0,1}}'

be32='{{1,1,-1,0,0,0,1},{0,-1,0,0,1,0,0},{0,0,-1,0,1,0,0},{-1,1,1,0,1,0,0},{-1,1,-1,1,0,0,0},{0,-1,1,1,0,0,1},{1,1,1,0,1,0,0}}'

be33='{{-1,1,0,1,0,1,0},{1,0,-1,1,0,0,-1},{-1,0,1,0,0,1,1},{2,0,1,0,0,1,0},{0,0,-1,0,0,0,1},{1,1,0,0,0,-1,1},{0,0,0,0,0,0,0}}'

be34='{{1,0,1,1,0,0,1},{1,1,-1,1,0,0,0},{0,0,-1,1,0,0,0},{-1,1,1,0,0,0,1},{-1,0,0,1,0,0,0},{-1,0,1,1,0,0,-1},{1,0,1,1,0,0,-1}}'

be35='{{0,0,0,0,0,0,0},{-1,1,0,1,1,-1,1},{1,1,-1,1,0,1,1},{0,-1,2,1,0,1,1},{0,1,1,-1,-1,-1,1},{0,0,0,0,0,0,0},{0,0,0,0,0,0,0}}'

be36='{{1,0,0,-1,0,2,0},{1,-1,0,1,0,0,-1},{0,0,0,0,0,0,0},{1,0,0,0,0,0,1},{0,1,0,1,-1,0,1},{-1,-1,0,0,0,1,1},{0,1,0,1,1,1,0}}'

be37='{{0,-1,0,1,-1,0,1},{0,1,1,1,1,-1,1},{1,1,0,0,1,1,0},{0,-1,0,0,1,0,0},{-1,0,1,-1,0,1,0},{0,0,0,0,0,0,0},{0,0,0,1,0,1,0}}'

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be39='{{-1,0,0,1,0,0,0},{1,0,-1,1,0,1,0},{1,-1,1,0,1,0,0},{0,0,0,1,0,-1,0},{0,1,0,1,1,1,0},{0,1,1,0,0,0,0},{-1,-1,1,0,0,1,0}}'

be40='{{0,1,1,0,0,-1,1},{0,1,0,1,0,0,0},{0,0,1,0,1,1,1},{0,0,0,1,1,0,0},{0,1,-1,-1,0,0,1},{0,1,0,-1,1,0,-1},{0,0,1,0,-1,0,0}}'

be41='{{1,-1,1,0,-2,1,0},{0,1,0,1,-1,1,0},{1,0,1,0,2,1,1},{0,0,0,0,0,0,0},{-1,0,1,0,0,0,0},{1,0,1,1,1,-1,-1},{0,0,0,0,0,0,0}}'

be42='{{2,1,0,0,0,-1,0},{1,-1,0,0,1,1,0},{0,0,0,0,0,0,0},{0,1,0,0,2,-1,0},{0,1,0,0,0,1,0},{0,-1,0,0,1,1,-1},{1,-1,0,0,0,1,1}}'

be43='{{0,0,0,0,0,0,0},{-1,0,-1,1,1,1,-1},{1,0,-1,0,0,0,0},{1,0,1,1,0,-1,0},{0,0,1,0,0,1,0},{0,1,0,1,0,1,1},{1,1,0,-1,1,0,0}}'

be44='{{0,0,1,1,1,1,0},{0,1,-1,0,-1,1,0},{-1,-1,0,1,1,0,0},{1,0,-1,1,1,0,0},{0,1,0,0,1,0,0},{0,0,0,1,-1,0,0},{0,1,1,0,0,0,0}}'

be45='{{0,0,1,0,0,-1,0},{0,1,1,1,1,0,0},{0,0,0,-1,1,0,0},{0,1,0,1,1,1,0},{0,1,0,-1,0,0,0},{0,0,1,0,-2,1,0},{0,-1,1,0,1,1,0}}'

be46='{{1,0,1,0,0,1,1},{0,1,0,1,0,1,1},{1,0,0,-1,0,0,0},{1,-1,-1,1,0,1,1},{0,0,0,0,0,1,-1},{0,0,0,-1,0,1,0},{-1,0,0,0,0,1,0}}'

be47='{{0,0,-1,-1,1,0,1},{0,0,0,0,0,0,0},{0,-1,1,1,0,0,1},{-1,1,0,0,-1,0,1},{0,0,2,-1,1,0,0},{0,1,0,0,1,0,0},{1,1,0,1,0,0,1}}'

be48='{{1,1,-1,0,0,0,-1},{1,-1,1,1,-1,0,1},{0,1,-1,1,0,0,1},{-1,0,1,1,0,0,-1},{1,1,2,1,1,0,0},{0,0,0,0,0,0,0},{0,0,0,0,0,0,0}}'

be49='{{0,0,0,0,0,0,0},{1,-1,0,1,1,0,0},{0,0,0,0,-1,1,0},{1,0,1,0,0,1,-1},{1,0,-1,-1,1,1,-1},{1,1,0,0,1,0,1},{0,0,0,0,0,1,1}}'

be50='{{1,0,1,1,-1,0,0},{0,0,0,0,0,0,0},{0,0,0,0,0,0,0},{1,-1,1,0,1,0,2},{-1,0,0,0,-1,1,1},{0,1,1,0,1,1,0},{-1,0,-1,1,0,0,1}}'

be51='{{1,0,0,-1,0,1,1},{0,0,0,0,0,1,-1},{-1,0,1,-1,1,0,0},{0,0,1,0,0,0,1},{1,0,-1,1,1,1,1},{0,0,1,1,0,0,0},{-1,0,0,0,0,1,0}}'

be52='{{0,0,0,0,0,-1,1},{0,0,-1,0,1,1,1},{0,1,0,0,1,-1,-1},{1,0,1,0,1,0,1},{0,0,0,0,0,0,0},{-1,-1,1,0,0,0,1},{0,2,1,0,-1,1,1}}'

be53='{{0,-1,0,0,0,0,1},{0,-1,0,1,0,0,0},{0,1,1,0,1,0,1},{0,0,1,1,1,0,-1},{0,1,1,0,-1,0,1},{0,0,-1,-1,1,0,1},{0,0,0,1,0,0,1}}'

be54='{{0,0,0,0,0,0,0},{0,-1,1,0,1,0,-1},{2,0,0,0,-1,0,-1},{1,1,-1,0,2,0,1},{0,1,0,0,0,0,-1},{0,1,1,0,-1,0,1},{1,0,1,0,1,0,1}}'

be55='{{-1,0,1,1,0,-1,0},{1,-1,1,0,-1,0,0},{0,1,1,0,0,0,0},{1,0,-1,1,0,0,1},{1,-1,1,0,1,0,0},{0,0,0,0,0,0,0},{0,1,1,0,0,1,1}}'

be56='{{1,1,0,0,0,0,0},{0,0,0,0,0,0,0},{1,0,-1,2,0,0,0},{-1,1,-1,0,0,1,0},{-1,0,0,1,0,-1,1},{0,1,1,0,0,1,1},{0,-1,1,1,0,1,0}}'

be57='{{0,1,1,1,0,0,-1},{1,0,0,0,0,1,0},{0,1,-1,0,0,1,-1},{1,1,0,0,0,-1,1},{1,0,0,1,0,0,0},{-1,0,0,1,0,1,1},{0,-1,0,1,0,0,0}}'

be58='{{1,0,0,0,1,1,1},{0,-1,1,0,0,1,1},{-1,0,0,0,1,0,0},{0,0,0,0,0,1,-1},{1,1,0,0,0,0,0},{0,1,0,0,1,0,0},{-1,1,-1,0,-1,1,1}}'

be59='{{0,0,0,0,0,0,0},{0,1,0,0,-1,0,0},{1,1,1,1,1,0,1},{0,0,1,0,1,-1,-1},{0,1,1,-1,1,0,0},{-1,1,0,0,1,1,0},{0,0,1,0,-1,0,0}}'

be60='{{0,0,0,-1,0,1,0},{0,0,1,1,1,1,0},{0,1,0,0,0,1,0},{0,1,-1,1,1,0,2},{0,-1,0,-1,1,0,1},{0,0,0,0,0,0,0},{0,-1,0,0,-1,1,1}}'

be61='{{0,0,0,0,0,0,0},{-1,0,0,1,-1,1,0},{1,1,0,2,0,0,0},{0,1,0,0,1,0,0},{1,0,1,-1,0,1,0},{-1,-1,0,1,1,0,0},{0,-1,1,1,1,0,0}}'

be62='{{-1,-1,1,0,0,0,1},{1,1,0,2,1,0,1},{1,0,0,0,-1,0,0},{1,0,0,-1,1,0,1},{0,0,0,0,0,0,0},{-1,1,0,0,0,0,0},{1,1,1,-1,1,0,-1}}'

be63='{{1,0,-1,0,-1,1,0},{-1,0,0,0,0,1,0},{0,1,-1,0,1,1,0},{1,0,0,0,1,0,0},{0,0,1,0,0,1,0},{0,1,0,1,-1,-1,0},{1,0,1,1,0,1,0}}'

be64='{{0,1,1,1,0,1,0},{-1,-1,0,1,0,0,1},{0,-1,1,0,1,0,-1},{0,0,0,0,1,0,1},{0,1,0,1,1,-1,0},{1,0,0,1,-1,0,1},{0,0,0,0,0,0,0}}'

be65='{{1,0,0,0,-2,1,0},{1,1,0,0,1,1,0},{1,0,0,1,1,0,-1},{0,0,0,1,0,-1,0},{0,0,0,1,1,1,1},{0,0,0,0,0,0,0},{1,-1,0,-1,1,0,0}}'

be66='{{-1,0,1,1,0,1,0},{0,0,0,0,0,0,0},{1,0,1,-1,1,-1,1},{0,0,-1,-1,-1,2,1},{1,0,0,1,1,1,0},{0,0,0,0,0,0,0},{1,0,1,0,-1,1,0}}'

be67='{{1,-1,-1,0,0,1,0},{1,0,0,-2,1,0,0},{0,0,0,0,0,0,0},{0,0,0,0,1,-1,0},{1,0,1,0,0,0,0},{0,0,1,1,1,1,0},{1,1,-1,1,1,1,0}}'

be68='{{0,0,0,0,0,0,0},{-1,1,0,-1,0,1,0},{1,1,0,0,0,0,0},{1,0,0,0,0,1,0},{0,1,0,1,1,0,-1},{0,0,0,1,0,1,2},{1,-1,0,-1,1,-1,1}}'

be69='{{0,0,0,0,0,0,0},{-1,1,0,1,-1,0,0},{1,1,1,0,0,1,0},{1,0,1,1,0,-1,0},{1,-1,0,0,0,0,0},{-1,0,1,0,1,1,0},{1,1,-1,0,0,1,0}}'

be70='{{0,0,0,0,0,0,0},{0,0,0,1,1,0,0},{0,-1,1,0,0,2,0},{1,1,-1,1,-1,1,0},{0,0,-1,-1,1,1,0},{0,1,0,0,1,0,0},{1,1,1,-1,0,0,0}}'

be71='{{0,0,0,0,0,0,0},{2,2,1,0,0,0,-1},{0,1,-1,0,1,0,-1},{0,1,0,0,0,0,1},{1,-1,0,1,1,0,0},{0,0,0,0,1,0,1},{1,-1,0,-1,1,0,0}}'

be72='{{2,0,-1,1,-2,0,0},{0,0,0,0,0,0,0},{1,0,1,2,1,1,0},{1,0,0,1,1,-1,0},{0,0,0,0,0,0,0},{1,1,1,-1,0,0,0},{-1,1,-1,1,0,0,0}}'

be73='{{0,0,1,0,1,-1,-1},{0,0,2,0,-1,1,0},{0,1,1,0,0,0,0},{0,-1,1,0,0,-1,1},{0,0,0,0,1,1,0},{0,1,0,0,0,0,1},{0,-1,1,0,1,0,1}}'

be74='{{1,1,1,-1,0,0,0},{0,0,1,0,0,0,1},{0,-1,1,0,0,0,0},{0,1,1,-1,0,0,-1},{0,1,1,2,0,0,0},{0,0,0,1,0,0,-1},{1,0,-1,1,0,0,1}}'

be75='{{1,1,1,1,1,-1,0},{1,0,1,1,0,1,0},{0,1,1,0,-1,0,1},{1,-1,0,0,0,0,0},{1,0,0,-1,0,0,0},{0,0,0,0,0,0,0},{0,1,1,-1,0,0,-1}}'

be76='{{1,1,0,1,-1,0,0},{1,1,-1,0,2,0,-1},{0,0,0,0,0,0,0},{0,-1,1,0,1,0,1},{1,0,0,0,0,0,1},{0,0,-1,0,0,0,1},{1,1,1,-1,0,0,0}}'

be77='{{0,1,0,1,0,0,0},{-1,0,1,1,0,0,-1},{1,0,0,1,-1,0,1},{0,1,0,0,1,0,0},{-1,0,0,0,0,0,1},{0,-1,1,0,1,0,1},{1,-1,0,1,1,0,0}}'

be78='{{0,0,0,0,0,0,0},{1,0,1,1,0,1,0},{1,0,1,-1,1,0,0},{0,0,-1,1,1,0,-1},{-1,0,1,0,0,1,1},{0,0,-1,0,0,1,0},{1,0,-1,1,0,-1,2}}'

be79='{{0,1,0,0,0,0,1},{0,0,1,-1,1,0,-1},{1,0,1,1,0,0,1},{0,1,0,1,1,0,-1},{0,0,0,0,0,0,0},{0,-1,0,0,2,0,1},{1,1,0,-1,0,0,-1}}'

be80='{{0,-1,0,1,1,1,0},{-1,1,1,0,1,0,0},{0,0,-1,1,1,1,0},{1,1,1,0,0,1,0},{0,0,0,-2,1,1,0},{0,1,-1,0,0,0,0},{0,0,0,0,0,0,0}}'

be81='{{1,0,1,1,-1,0,0},{1,0,1,0,1,0,-1},{0,-1,0,1,1,0,1},{1,0,-1,0,0,0,0},{0,0,0,0,0,0,0},{1,0,0,-1,0,0,2},{0,1,-1,1,1,0,0}}'

be82='{{1,-1,1,0,1,0,0},{0,1,-1,1,0,0,1},{-1,0,1,1,1,1,-1},{0,0,0,0,0,0,0},{0,0,0,0,1,0,1},{0,1,1,0,0,0,0},{0,-1,0,0,-1,1,1}}'

be83='{{1,0,0,-1,0,1,-1},{1,0,0,-1,1,1,0},{1,0,0,0,0,-1,0},{-1,0,0,0,2,-1,0},{0,0,0,1,0,1,0},{1,0,0,0,1,1,1},{1,0,0,1,0,0,0}}'

be84='{{0,1,0,1,1,0,1},{0,1,0,-1,0,0,0},{1,-1,0,-1,1,0,2},{0,0,1,-1,-1,0,1},{0,1,0,1,-1,0,1},{0,0,0,0,0,0,0},{1,0,1,1,0,0,-1}}'

be85='{{0,0,0,1,1,-1,1},{0,0,0,-1,0,1,0},{0,-1,0,1,-1,1,0},{0,1,0,-1,-1,0,1},{0,1,1,1,0,1,0},{0,1,-1,1,0,1,0},{0,0,0,0,1,1,0}}'

be86='{{0,1,-1,0,0,-1,1},{0,0,-1,0,1,1,1},{0,1,1,0,2,-1,-1},{0,0,1,0,-1,0,0},{0,-1,0,0,1,0,0},{0,1,2,0,1,1,1},{0,0,0,0,0,0,0}}'

be87='{{0,1,0,1,-1,1,2},{0,0,0,0,1,0,1},{1,1,0,-1,0,0,-1},{1,0,0,1,0,0,0},{-1,0,0,0,1,1,-1},{0,0,0,1,0,0,-1},{1,0,0,0,1,0,0}}'

be88='{{0,1,1,0,1,0,1},{0,0,0,0,0,0,0},{1,-2,0,0,2,-1,0},{0,1,-1,0,1,0,1},{1,1,0,0,0,1,-1},{0,-1,0,0,0,1,0},{0,0,0,0,0,1,1}}'

be89='{{1,0,-1,0,2,0,0},{-1,1,-1,1,0,2,0},{1,0,1,0,0,2,0},{0,0,1,1,1,-1,0},{0,0,0,0,0,0,0},{0,0,0,0,0,0,0},{-1,-1,0,0,1,1,0}}'

be90='{{0,1,0,1,0,0,0},{0,-1,1,1,1,0,0},{0,0,0,-1,0,0,1},{0,1,0,0,-1,1,-1},{0,0,0,0,0,0,0},{0,-1,-1,1,1,1,1},{0,2,0,0,1,0,1}}'
map(finnKG,[be26])
[(10, 14.109430218654275, 1.4109430218654275)]
be1='{{0,0,1,-1,1,1,0},{-1,0,1,1,-1,0,0},{0,1,1,0,0,0,-2},{0,0,0,0,0,0,0},{1,1,1,0,-1,1,1},{0,1,0,2,1,1,1},{0,1,0,0,0,-1,0}}'

be2='{{0,-1,0,0,1,1,1},{1,0,-1,1,0,1,0},{1,0,1,0,-1,-1,0},{-1,0,0,1,1,0,-1},{0,0,0,-1,1,0,0},{1,0,1,1,1,0,0},{0,1,1,0,1,1,0}}'

be3='{{0,1,0,0,0,-1,2},{0,0,0,0,0,0,0},{-1,0,-1,1,0,1,0},{1,1,0,-1,0,1,0},{-1,1,1,0,0,1,0},{0,-1,0,0,1,1,1},{1,0,0,2,-1,1,1}}'

be4='{{0,0,1,-1,0,0,0},{1,0,-1,-1,1,0,0},{0,0,0,1,1,1,-1},{0,0,1,2,1,-1,1},{2,0,1,1,-1,0,-1},{0,0,0,0,1,-1,0},{1,0,0,0,1,1,1}}'

be5='{{0,0,0,0,0,0,0},{0,1,-1,0,0,1,1},{0,1,0,1,0,0,0},{2,0,0,0,0,-1,1},{0,-1,0,1,-1,0,1},{1,1,2,-1,0,1,0},{-1,0,1,1,1,-1,1}}'

be6='{{1,-1,0,0,0,0,0},{1,1,1,0,1,1,1},{0,0,0,0,0,0,0},{-1,-1,0,2,0,1,1},{1,0,0,-2,-1,1,1},{1,0,-1,1,0,0,1},{1,1,0,1,0,-1,0}}'

be7='{{0,0,0,0,-1,1,0},{0,1,0,1,1,1,0},{-1,0,1,1,0,0,-1},{0,0,1,1,0,-1,1},{0,1,0,-1,-1,0,1},{0,0,-1,2,0,0,1},{1,0,1,0,1,1,0}}'

be8='{{0,0,1,-1,1,1,0},{0,1,0,0,-1,1,1},{0,1,0,1,-1,-1,0},{0,0,1,1,0,-1,1},{0,1,0,1,2,0,0},{0,-1,0,1,0,1,1},{0,0,0,-1,1,-1,1}}'

be9='{{-1,1,2,1,0,-1,0},{1,0,1,0,0,2,0},{-1,0,-1,1,0,1,0},{0,0,1,0,0,0,1},{1,0,0,1,0,-1,1},{0,1,-1,0,0,1,1},{0,0,0,-1,0,0,1}}'

be10='{{1,1,0,1,0,0,-1},{0,1,-1,-1,0,1,2},{0,0,-1,0,1,1,-1},{1,0,1,-1,1,0,0},{0,0,0,0,1,0,1},{0,0,0,1,1,-1,1},{0,0,1,0,0,1,0}}'

be11='{{0,1,0,1,-1,0,1},{1,1,-1,0,1,0,0},{1,0,0,0,-1,0,0},{0,1,2,0,1,-1,1},{1,-1,2,1,0,0,-1},{-1,0,1,0,0,1,1},{0,0,0,0,0,0,0}}'

be12='{{1,0,-1,1,1,1,-1},{1,0,1,0,0,0,0},{-1,0,-1,2,1,2,1},{0,0,0,0,0,0,0},{-1,0,1,-1,2,-1,0},{0,0,1,2,0,-1,0},{0,0,1,0,0,1,0}}'

be13='{{1,-1,0,0,-1,0,1},{0,1,1,1,1,0,2},{2,0,1,-1,0,0,0},{-1,0,1,0,1,0,-1},{1,1,-1,1,0,0,0},{0,-1,0,1,0,0,0},{1,0,0,0,1,0,0}}'

be14='{{0,0,1,1,0,1,1},{0,1,0,-1,1,0,1},{0,2,1,1,0,0,-2},{0,1,0,1,0,-1,1},{0,0,-1,1,0,0,0},{0,1,0,0,0,1,0},{0,-1,-1,1,1,1,-1}}'

be15='{{-1,0,1,1,1,0,0},{1,0,-1,2,0,1,-1},{1,0,0,1,0,-1,1},{1,-1,1,0,0,1,0},{0,0,0,0,0,0,0},{0,2,0,0,0,1,1},{0,-1,-1,0,1,0,1}}'

be16='{{0,1,0,0,-1,1,1},{0,0,0,0,-1,0,1},{0,0,0,0,1,1,0},{0,-1,2,1,0,1,1},{0,1,1,-1,1,0,0},{0,0,-1,1,1,0,1},{0,1,0,1,-1,1,-2}}'

be17='{{-1,0,0,1,0,0,2},{0,1,1,-1,1,0,0},{0,0,0,0,0,0,0},{1,-1,0,0,0,0,0},{-1,1,-1,1,1,0,-1},{1,2,1,1,-1,0,0},{2,1,-1,0,1,0,1}}'

be18='{{1,1,1,0,1,0,0},{0,0,1,1,0,-1,1},{-1,0,0,1,0,1,1},{-1,0,1,0,0,0,0},{1,0,0,1,-1,0,1},{0,0,0,2,0,0,-2},{0,1,-1,1,0,0,1}}'

be19='{{0,0,0,1,1,1,1},{-2,1,1,1,1,-1,1},{0,0,0,0,0,0,0},{0,1,-1,0,-1,0,1},{2,1,1,0,1,0,1},{0,0,0,1,-1,0,0},{0,1,1,-1,-1,0,0}}'

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be94='{{0,0,0,0,0,0,0},{-1,0,0,0,0,1,2},{1,0,0,1,-1,1,0},{1,1,1,-1,0,0,0},{0,0,0,1,1,1,-1},{0,0,1,2,1,-1,1},{1,-1,0,-1,1,0,0}}'

be95='{{0,0,1,0,1,1,1},{1,-1,0,0,2,1,-1},{0,1,0,0,-1,1,-1},{1,0,0,0,-1,1,1},{-1,0,0,0,0,1,0},{0,1,0,0,1,-1,1},{1,1,1,0,0,0,-1}}'

be96='{{0,1,1,-1,1,0,0},{0,1,1,0,1,1,0},{1,-1,-1,0,2,-1,0},{0,-1,1,0,0,0,0},{0,0,-1,0,0,1,0},{2,0,0,0,-1,1,0},{1,0,1,1,1,0,0}}'

be97='{{-1,0,-1,0,1,1,0},{1,0,0,0,1,0,0},{0,0,1,0,1,1,-1},{0,0,0,0,1,-1,0},{1,1,0,1,0,1,0},{1,0,0,-1,1,1,2},{0,-1,0,0,1,1,-1}}'

be98='{{0,1,-1,0,1,0,1},{1,0,0,0,0,0,1},{1,1,0,0,-1,1,0},{0,1,1,-1,-1,0,0},{0,-1,1,-1,1,1,1},{-1,0,1,1,0,0,1},{1,0,0,1,0,0,0}}'

be99='{{1,2,-1,0,1,-1,0},{1,1,1,0,0,0,-1},{-1,1,0,0,0,0,0},{-1,0,1,0,1,1,-2},{0,0,1,0,0,0,1},{-1,1,0,0,0,1,1},{1,1,0,0,0,1,1}}'

be100='{{1,0,1,0,0,-1,1},{-1,0,1,0,0,0,0},{1,0,-1,1,1,1,1},{-1,0,0,0,1,1,1},{0,0,0,0,0,0,0},{1,0,0,-2,-1,2,0},{1,0,1,1,1,1,-1}}'

be101='{{1,0,2,0,-1,-1,-1},{0,0,0,0,1,-1,0},{1,0,0,1,0,0,0},{-1,0,1,1,0,0,1},{2,0,0,0,1,0,1},{0,0,1,-1,1,1,0},{1,0,0,1,0,1,-1}}'

be102='{{0,0,1,-1,0,1,1},{0,0,-1,0,1,0,0},{1,0,1,2,0,-1,1},{-1,0,0,1,1,2,-1},{1,0,0,0,0,1,0},{1,0,0,0,1,0,0},{0,0,-1,0,-1,1,1}}'
map(finnKG,[be1,be2,be3,be4,be5,be6,be7,be8,be9,be10,be11,be12,be13,be14,be15,be16,be17,be18,be19,be20,be21,be22,be23,be24,be25,be26,be27,be28,be29,be30,be31,be32,be33,be34,be35,be36,be37,be38,be39,be40,be41,be42,be43,be44,be45,be46,be47,be48,be49,be50,be51,be52,be53,be54,be55,be56,be57,be58,be59,be60,be61,be62,be63,be64,be65,be66,be67,be68,be69,be70,be71,be72,be73,be74,be75,be76,be77,be78,be79,be80,be81,be82,be83,be84,be85,be86,be87,be88,be89,be90,be91,be92,be93,be94,be95,be96,be97,be98,be99,be100,be101,be102])
[(12, 16.49169729267991, 1.3743081077233257), (12, 16.59295656117907, 1.3827463800982558), (12, 15.81173181999209, 1.3176443183326743), (12, 16.50859936713224, 1.3757166139276868), (12, 16.124224480035547, 1.3436853733362957), (12, 16.588115100347355, 1.3823429250289463), (12, 16.707860052376322, 1.3923216710313602), (12, 16.348958878488784, 1.3624132398740654), (12, 16.203465536619984, 1.350288794718332), (12, 16.11894751941488, 1.3432456266179067), (12, 16.300011300686762, 1.3583342750572303), (12, 16.145995310151537, 1.3454996091792948), (12, 16.730797302920596, 1.3942331085767163), (12, 16.502189421141072, 1.375182451761756), (12, 15.617391426025456, 1.3014492855021214), (12, 16.41680375515465, 1.3680669795962208), (12, 15.635768123260075, 1.3029806769383396), (12, 16.577915260602058, 1.3814929383835048), (12, 16.64665480284461, 1.387221233570384), (12, 16.434768396805303, 1.3695640330671086), (12, 16.61218012737696, 1.38434834394808), (12, 16.352747079030074, 1.3627289232525062), (12, 15.957872339488006, 1.3298226949573337), (12, 16.415652220783652, 1.3679710183986378), (12, 16.54708827769622, 1.3789240231413515), (12, 16.424536656185797, 1.368711388015483), (12, 16.6528453029406, 1.3877371085783834), (12, 16.30277429946384, 1.3585645249553202), (12, 16.172799436390406, 1.347733286365867), (12, 15.677324276856561, 1.3064436897380467), (12, 16.372285226775357, 1.3643571022312797), (12, 16.4424943753667, 1.3702078646138915), (12, 16.475051711010035, 1.372920975917503), (12, 16.60239148585431, 1.3835326238211925), (12, 16.216270538888544, 1.351355878240712), (12, 15.909840695298094, 1.3258200579415078), (12, 16.451183191081483, 1.3709319325901237), (12, 16.704971709590833, 1.392080975799236), (12, 16.515686274515566, 1.376307189542964), (12, 16.592044179210685, 1.382670348267557), (12, 16.370511914079007, 1.3642093261732506), (12, 16.449100918932654, 1.3707584099110546), (12, 16.310810039680415, 1.3592341699733679), (12, 16.44183171427822, 1.3701526428565183), (12, 16.706642226919513, 1.392220185576626), (12, 15.968934240686153, 1.3307445200571795), (12, 16.11135921069728, 1.3426132675581066), (12, 16.528761754013654, 1.3773968128344711), (12, 16.7309350689235, 1.3942445890769584), (12, 16.54405186569694, 1.3786709888080784), (12, 16.28218741643726, 1.3568489513697717), (12, 16.386897662918205, 1.3655748052431838), (12, 16.820036679014727, 1.4016697232512272), (12, 16.262252315664437, 1.3551876929720363), (12, 16.245367248441013, 1.353780604036751), (12, 14.966629546743148, 1.2472191288952623), (12, 16.652106444931714, 1.3876755370776428), (12, 16.033712002350047, 1.3361426668625038), (12, 16.602762060784784, 1.3835635050653987), (12, 16.521254005040902, 1.3767711670867417), (12, 15.810712128514984, 1.3175593440429154), (12, 16.503779458880228, 1.3753149549066856), (12, 16.370735475561894, 1.3642279562968245), (12, 16.173694524440275, 1.3478078770366897), (12, 15.929840501800612, 1.3274867084833843), (12, 15.931773723929446, 1.3276478103274538), (12, 15.883697960262785, 1.3236414966885655), (12, 16.3722422019604, 1.3643535168300334), (12, 16.712808129078283, 1.3927340107565236), (12, 16.820036679014727, 1.4016697232512272), (12, 16.560243666438538, 1.3800203055365448), (12, 16.362764290045895, 1.363563690837158), (12, 16.60143110210339, 1.3834525918419491), (12, 16.526021375118745, 1.377168447926562), (12, 16.26493229175808, 1.3554110243131732), (12, 16.376885567620093, 1.3647404639683411), (12, 16.505568126785317, 1.375464010565443), (12, 16.470913624602456, 1.372576135383538), (12, 16.063372045739992, 1.3386143371449994), (12, 16.762163021072137, 1.3968469184226782), (12, 16.642608852760272, 1.386884071063356), (12, 16.23378173727126, 1.3528151447726051), (12, 16.50556812678532, 1.3754640105654434), (12, 16.70659863212888, 1.3922165526774066), (12, 16.529332809594276, 1.377444400799523), (12, 16.522891678954334, 1.3769076399128612), (12, 15.960257690705317, 1.330021474225443), (12, 16.553677715574114, 1.3794731429645095), (12, 15.80988493191988, 1.3174904109933234), (12, 16.377740934747607, 1.3648117445623005), (12, 16.273302071916717, 1.3561085059930598), (12, 16.598189315540232, 1.383182442961686), (12, 16.45699373074277, 1.3714161442285642), (12, 15.632072750194267, 1.3026727291828555), (12, 15.937093202726864, 1.3280911002272386), (12, 16.613154647616206, 1.3844295539680171), (12, 16.606082565940728, 1.383840213828394), (12, 16.45496166512379, 1.3712468054269824), (12, 16.72682111136423, 1.3939017592803526), (12, 15.80480471546068, 1.3170670596217233), (12, 15.70106797220566, 1.3084223310171383), (12, 16.369376512599743, 1.364114709383312)]
be1='{{1,0,-1,1,0,0,1},{1,0,2,0,0,0,1},{1,0,-1,0,1,0,-1},{0,0,0,0,0,0,0},{0,0,0,0,1,0,1},{0,0,1,0,1,1,-1},{-1,0,1,1,1,-1,-1}}'

be2='{{-1,1,0,1,0,0,1},{0,1,1,-1,-1,0,0},{0,0,0,0,0,0,0},{1,0,1,1,0,0,1},{0,0,0,0,1,0,1},{0,1,0,-1,1,1,0},{0,1,0,0,1,-1,-1}}'

be3='{{0,-1,1,0,1,0,1},{-1,0,-1,0,0,1,1},{0,0,0,0,0,0,0},{0,1,1,1,0,1,0},{1,1,0,0,1,0,1},{0,-1,-1,1,1,0,0},{0,0,0,0,1,0,-1}}'

be4='{{-1,-1,1,0,1,0,0},{0,1,0,0,0,-1,0},{0,0,0,0,0,1,1},{1,1,1,0,0,0,1},{0,0,0,0,0,0,0},{1,1,0,1,1,1,-1},{-1,0,0,1,0,-1,1}}'

be5='{{-1,0,0,0,0,1,0},{0,1,0,1,1,0,1},{0,-1,0,0,0,1,0},{0,0,0,0,0,1,1},{1,1,0,-1,0,1,0},{-1,1,0,0,0,1,-1},{1,0,0,0,1,1,-1}}'

be6='{{-1,-1,0,1,1,0,0},{-1,1,0,1,0,0,1},{0,0,0,1,0,0,-1},{1,0,0,1,0,-1,1},{0,0,0,0,0,0,0},{0,-1,0,0,0,2,1},{1,1,0,0,1,1,0}}'

be7='{{0,-1,-1,0,0,1,1},{-1,1,0,0,1,0,1},{0,0,0,0,0,0,0},{1,0,-1,0,2,1,-1},{1,0,1,0,1,0,1},{1,0,0,0,0,-1,0},{0,0,1,0,0,1,0}}'
map(finnKG,[be1,be2,be3,be4,be5,be6,be7])
[(10, 13.900424464904647, 1.3900424464904648), (10, 13.975630543335862, 1.3975630543335862), (10, 13.984147391552417, 1.3984147391552417), (10, 14.03507604460128, 1.403507604460128), (10, 13.944458822883936, 1.3944458822883936), (10, 13.390717458339262, 1.3390717458339263), (10, 13.701735487708977, 1.3701735487708977)]
be1='{{0,0,0,0,0,0},{-1,1,0,1,0,1},{0,0,1,1,1,-1},{0,1,1,-1,0,1},{0,1,0,0,0,-1},{1,1,0,1,-1,0}}'

be2='{{-1,-1,1,0,1,0},{-1,2,1,0,0,0},{0,0,0,0,0,0},{1,1,0,0,1,1},{1,0,1,0,1,-1},{0,0,1,0,-1,0}}'

be3='{{1,1,0,0,0,0},{0,1,1,0,-1,-1},{0,1,0,0,1,0},{1,0,0,0,0,1},{-1,0,1,0,1,1},{-1,1,0,0,-1,1}}'

be4='{{-1,0,1,0,-1,1},{0,1,-1,0,0,0},{0,1,0,-1,1,1},{0,0,0,0,0,0},{0,1,1,1,1,0},{1,1,1,0,-1,0}}'

be5='{{0,1,0,0,0,1},{0,-1,1,-1,0,1},{0,0,0,0,0,0},{-1,0,1,1,0,1},{0,1,1,0,1,-1},{1,1,1,0,-1,0}}'

be6='{{0,0,0,1,1,0},{-1,1,-1,1,0,0},{0,1,-1,-1,1,0},{1,1,0,1,-1,0},{0,1,2,0,1,0},{0,0,0,0,0,0}}'
map(finnKG,[be1,be2,be3,be4,be5,be6])
[(8, 11.262193670874126, 1.4077742088592657), (8, 11.103546255013217, 1.3879432818766522), (8, 11.262193670874131, 1.4077742088592664), (8, 11.262193670874126, 1.4077742088592657), (8, 11.26219367087413, 1.4077742088592662), (8, 11.103546255013216, 1.387943281876652)]
be1='{{0,-1,-1,1,1,1,1},{0,1,0,-1,0,-1,1},{0,0,0,0,0,0,0},{-1,1,1,1,0,0,0},{0,-1,1,0,0,0,0},{0,1,1,-1,2,1,0},{1,1,0,2,1,-1,0}}'

be2='{{1,-1,0,1,-1,0,2},{1,1,0,0,0,0,0},{0,0,0,-1,1,-1,1},{1,1,0,1,1,1,1},{-1,0,0,0,1,1,1},{1,0,0,0,0,0,-1},{-1,1,0,1,0,-1,0}}'
be1='{{0,0,0,0,0,0,0},{0,1,1,-1,1,0,0},{1,-1,1,-1,1,0,1},{0,0,0,2,1,0,1},{0,0,0,0,0,0,0},{0,0,1,1,0,1,-1},{1,0,1,1,-1,-1,-1}}'
map(finnKG,[be1])
[(10, 13.887539114488066, 1.3887539114488066)]
be1='{{0,-1,1,0,0,0,0},{1,1,1,-1,-1,1,0},{0,1,0,0,1,1,1},{1,0,-1,0,0,0,0},{0,0,0,0,0,0,0},{1,1,1,1,0,1,-1},{1,0,0,0,0,-1,0}}'

be2='{{1,0,0,1,1,-1,0},{-1,1,0,0,1,1,0},{1,0,0,0,0,1,0},{1,0,0,1,1,1,0},{1,0,0,-2,1,0,0},{-1,-1,0,0,1,1,0},{0,0,0,0,1,-1,0}}'

be3='{{-1,0,1,0,0,0,0},{-1,1,-1,0,0,1,0},{0,0,1,0,0,1,0},{0,0,-1,0,0,0,1},{1,0,0,1,0,1,1},{1,0,1,-1,0,0,1},{0,1,1,0,0,-1,1}}'

be4='{{0,-1,0,1,0,-1,1},{-1,1,0,1,0,1,0},{0,-1,0,-1,0,1,1},{0,0,0,0,0,0,0},{1,2,0,1,0,0,2},{0,-1,0,1,0,1,1},{0,0,0,1,0,0,-1}}'
map(finnKG,[be1,be2,be3,be4])
[(10, 14.058368450886839, 1.4058368450886838), (10, 13.680838829676365, 1.3680838829676365), (10, 14.008496665709206, 1.4008496665709207), (10, 13.818449703331881, 1.381844970333188)]

map(finnKG,[be6,be9])
[(10, 14.142135622543694, 1.4142135622543694), (10, 14.142135622543693, 1.4142135622543692)]
be1='{{0,-2,1,0,0,1},{-1,2,1,0,1,1},{0,1,0,0,-1,0},{0,0,1,1,-1,1},{1,1,0,1,1,0},{0,0,1,0,0,-1}}'

be2='{{-1,0,0,1,1,1},{-1,1,0,0,0,0},{2,1,0,0,1,2},{0,0,0,0,1,-1},{1,1,0,0,1,-1},{1,1,0,1,-2,-1}}'

be3='{{0,0,0,0,0,0},{-2,2,0,1,-1,0},{1,1,0,1,-1,0},{1,0,-1,1,1,0},{1,2,1,0,2,0},{1,1,0,-1,-1,0}}'

be4='{{0,0,-1,1,0,0},{1,1,-1,0,0,1},{1,1,0,-1,1,0},{0,0,1,1,1,1},{-1,1,0,0,1,-1},{1,1,1,1,-1,-1}}'

be5='{{0,0,1,1,1,1},{0,1,0,-1,0,2},{0,0,1,1,0,0},{1,-1,1,-1,0,0},{0,1,0,-1,1,-1},{1,1,-1,1,0,0}}'

be6='{{1,-1,1,0,1,0},{-1,1,0,0,1,1},{2,1,-1,1,0,1},{0,0,1,0,-1,0},{0,0,1,1,1,-1},{0,1,0,0,0,-1}}'

be7='{{-1,-1,1,0,1,0},{1,1,0,0,1,-1},{0,1,2,0,0,1},{2,0,0,0,1,1},{1,-1,0,0,0,0},{1,0,1,0,-1,-1}}'

be8='{{0,-1,0,1,1,1},{1,1,-1,0,0,1},{1,-1,0,0,0,0},{1,1,1,0,1,0},{-2,0,0,0,1,1},{1,0,0,-1,1,1}}'

be9='{{0,0,1,-1,1,1},{-2,1,0,0,1,0},{1,0,0,1,1,1},{0,1,0,0,0,1},{1,1,1,0,0,-1},{0,1,0,0,-1,0}}'

be10='{{-1,1,0,1,1,0},{0,1,0,-1,1,1},{0,1,0,-1,0,0},{1,-1,0,0,1,1},{1,1,0,1,2,-1},{1,1,0,0,-1,-1}}'

be11='{{0,-1,0,1,1,1},{-1,2,0,0,1,2},{1,0,0,0,0,1},{1,1,0,1,0,-1},{0,0,0,0,-1,1},{-1,0,0,2,-1,0}}'
map(finnKG,[be1,be2,be3,be4,be5,be6,be7,be8,be9,be10,be11])
[(10, 13.675658437033482, 1.3675658437033482), (10, 13.685707858311686, 1.3685707858311686), (10, 13.759050146932703, 1.3759050146932703), (10, 13.416407864946457, 1.3416407864946458), (10, 13.190802734009278, 1.3190802734009277), (10, 13.885509877034453, 1.3885509877034452), (10, 13.150529301132378, 1.3150529301132379), (10, 13.971156239493608, 1.3971156239493607), (10, 13.405993735082342, 1.3405993735082342), (10, 13.758783065009299, 1.37587830650093), (10, 12.960999194966533, 1.2960999194966534)]

















map(finnKG,[be14])

map(finnKG,[be1])
WARNING: Some output was deleted.
























map(finnKG,[be1])
[(8, 11.262193104312297, 1.4077741380390372)]












be180='{{0,0,0,0,0,0,0,0},{1,1,0,0,1,1,0,0},{0,0,-1,0,1,0,0,0},{0,0,0,-1,0,1,0,0},{1,0,0,1,-1,0,0,1},{0,1,1,0,0,-1,1,0},{0,0,1,1,1,0,-1,0},{0,0,1,1,0,1,0,-1}}'
map(finnKG,[be180])
[(12, 16.9705624961966, 1.4142135413497166)]