The realization space is
  [1   1   0                    x2 - 1   0   1   1            0                    x2 - 1    1    1]
  [1   0   1   -x1*x2 - x1 + x2^2 - x2   0   1   0           x2   -x1*x2 - x1 + x2^2 - x2   x1   x1]
  [0   0   0                         0   1   1   1   -x1 + 2*x2        -x1*x2 + x2^2 - x2   x1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1 - x2, x1, x2, 2*x1 - x2 + 1, x1^2 - 2*x1*x2 - x1 + x2^2 - x2, x1 - x2 + 1, x1^2 - 2*x1*x2 + x1 + x2^2 - 2*x2 + 1, 2*x1^2 - 4*x1*x2 + x1 + 2*x2^2 - 2*x2, x1^2 - 2*x1*x2 - x1 + x2^2 + 2*x2, x1 - 2*x2, 2*x1^2 - 5*x1*x2 + x1 + 3*x2^2 - 3*x2, x1 - x2 - 1, x1 + x2 - 1, x2 - 1, x1 - x2 + 2, x1*x2 + x1 - x2^2 + 2*x2 - 1, x1*x2 + x1 - x2^2 + x2, x1^2 + 2*x1*x2 - x1 - x2^2 + x2, 2*x1*x2 - x1 - x2^2 + x2, 2*x1^2 - 3*x1*x2 + x2^2 - x2, x1^2 - x1*x2 - x1 + 2*x2, x1^2 - x1*x2 - x2, 2*x1 - 1, x1^2*x2 + x1^2 - x1*x2^2 - x1*x2 + x2^2 - x2, x1^2*x2 + x1^2 - 2*x1*x2^2 - x1 + x2^3 - 3*x2^2 + 2*x2, x1^2*x2 + x1^2 - 2*x1*x2^2 - x1*x2 + x2^3 - x2^2, x1^2*x2 + x1^2 - 2*x1*x2^2 - x1 + x2^3 - 2*x2^2 + x2, x1^2*x2 + x1^2 - 2*x1*x2^2 - x1*x2 + x2^3 - x2, 2*x1*x2 + x1 - 2*x2^2 + 3*x2 - 1, x1*x2 - x2^2 + 2*x2 - 1, x1 - 3*x2, x1^2*x2 + x1^2 - 3*x1*x2^2 - x1*x2 + 2*x2^3 - x2^2 - x2, x1^2*x2 + x1^2 - 3*x1*x2^2 - x1 + 2*x2^3 - 3*x2^2 + x2]