The realization space is
  [1   1   0   0   1   1    0    1    2     2     1]
  [0   1   1   0   0   1    2    2    4   -x1   -x1]
  [0   0   0   1   1   1   x1   x1   x1    x1    x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^2 + 2*x1 - 4, -4*x1^5 - 20*x1^4 + 16*x1^3 + 144*x1^2 + 64*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 2, x1 + 2, x1 + 4, x1 + 3, x1^2 + x1 - 4, x1 - 1, x1^2 + 2*x1 - 2, x1^2 + 3*x1 - 2, x1 + 1, x1 - 2, x1^2 + 4*x1 - 4, x1 - 4]