The realization space is
  [1   1   x1 - 1   0   0   1    1     x1 - 1    0    1    1]
  [0   1       -1   1   0   0    1         -1    1   -1   -1]
  [0   0        0   0   1   1   x1   2*x1 - 2   -2    2   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^7 + 28*x1^6 - 68*x1^5 + 36*x1^4 + 120*x1^3 - 208*x1^2 + 96*x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 2, 2, x1 - 4, x1^2 - 3*x1 + 4, x1 - 3, x1, x1 - 1, x1 + 2, x1^2 - x1 + 2, x1 + 1, 3*x1 - 2]