We have seen in section 4.1 that with positive kinematic data all the solutions we obtain are real . This means we can analyze them by counting bounded chambers in RP 2 space when |147| , |257| and |367| vanish . We expect to find 12 bounded chambers , which would correspond to the 12 solutions for each of the 15 existing configurations . The bounded chambers come in the following way . First , we use the same gauge fixing for the first four particles as explained in section 4.1 . This creates 5 repelling lines , one of them crossing the diagonal of the square [ 0 , 1 ] 2 created by particles 1 and 4 . It is precisely on this line where the soft particle 7 must be . We can have solutions where particle 7 is outside the square [ 0 , 1 ] 2 , since particles 5 and 6 can simultaneously create bounded chambers for each other . We represent this situation in figure A.9 . Left : the first four particles are gauge - fixed . This creates 5 repelling lines , drawn in black , and particle 7 must be on the line that passes through 1 and 4 . Center : we now consider the situation in which the soft particle 7 is in the outside - right(left ) of the square [ 0 , 1 ] 2 . Right : particles 5 and 6 must lie on the blue dashed lines created by particles 7 , 2 and 3 . This only happens if both particles bound each other through particle 4(1 ) ( red and orange lines ) . The two grey bounded chambers are those where particles 5 and 6 can be . This configuration gives rise to 2 different solutions , since particles 5 and 6 can bound each other through particles 1 and 4 when particle 7 is outside the square [ 0 , 1 ] 2 .