The realization space is
  [1   1   0   x2 - 1   0   1   1    0   x1*x2 - x1 - x2 + 1    1    1]
  [1   0   1      -x1   0   1   0   x1            -x1^2 + x1   x2   x1]
  [0   0   0        0   1   1   1   x2            -x2^2 + x2   x2   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[x2, x1 - x2, x2 - 1, x1, x1 + x2 - 1, x1 - 1, x1^2 + x1*x2 - 2*x1 - x2^2 + x2, x1 + x2^2 - x2, x1^2 - x1*x2 - x1 - x2^2 + x2, x1*x2 - 2*x1 - x2 + 1, x1 - x2 + 1, x1*x2 - 2*x1 - x2^2 + x2, x1*x2 - x1 - x2^2, 2*x2 - 1, x1^2 - x1 - x2 + 1, x1 - x2^2 + x2 - 1, x1^2 + x1*x2 - 2*x1 + x2^2 - 2*x2 + 1, x1 + x2]