The realization space is
  [1   1   x1 + 1   0   0   1     1      x1 + 1   0    1   2]
  [1   0       x1   1   0   1     0          x1   1   x1   1]
  [0   0        0   0   1   1   -x1   x1^2 + x1   2   x1   2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^5 + 2*x1^4 - 12*x1^3 + 8*x1^2)
avoiding the zero loci of the polynomials
RingElem[3*x1 - 2, x1, 3*x1 - 1, x1 - 1, 2*x1 - 1, 2, x1 + 2, x1 + 1, x1 - 2, x1^2 + x1 + 2, x1^2 + 1]