/*  

 N=12
 M=5

 unique solution

 length of multipoles: 
   [ 1/13, 0, 0, 0, 0, 0, 121/323, 0, 0, 0, 147/391, 0, 980/5681 ]

 cumulative squared lengths A_M:
   [ 0, 0, 0, 0, 0, 121/323, 121/323, 121/323, 121/323, 328/437, 328/437, 12/13 ]

 dodecaeder

 symmetry group Z_2 x A_5

 configuration:
   [  0.000000000000000000000000000000,  0.000000000000000000000000000000,  1.00000000000000000000000000000 ],
   [  0.894427190999915878563669467490,  0.000000000000000000000000000000, -0.447213595499957939281834733747 ],
   [ -0.723606797749978969640917366874,  0.525731112119133606025669084849, -0.447213595499957939281834733745 ],
   [ -0.723606797749978969640917366874, -0.525731112119133606025669084849, -0.447213595499957939281834733745 ],
   [ -0.276393202250021030359082633127,  0.850650808352039932181540497063,  0.447213595499957939281834733746 ],
   [ -0.276393202250021030359082633127, -0.850650808352039932181540497063,  0.447213595499957939281834733746 ],
   [  0.276393202250021030359082633127,  0.850650808352039932181540497061, -0.447213595499957939281834733747 ],
   [  0.276393202250021030359082633127, -0.850650808352039932181540497061, -0.447213595499957939281834733747 ],
   [  0.723606797749978969640917366873,  0.525731112119133606025669084847,  0.447213595499957939281834733746 ],
   [  0.723606797749978969640917366873, -0.525731112119133606025669084847,  0.447213595499957939281834733746 ],
   [ -0.894427190999915878563669467493,  0.000000000000000000000000000000,  0.447213595499957939281834733746 ],
   [  0.000000000000000000000000000000,  0.000000000000000000000000000000, -1.00000000000000000000000000000 ]


*/

psi12:=[ 0, 1/5*sqrt(7), 0, 0, 0, 0, 1/5*sqrt(11), 0, 0, 0, 0, -1/5*sqrt(7), 0 ];