The realization space is
  [1   1   0   x1^2 - x1 + x2   0   1   1                0        x1^2 - x1 + x2        x1^2 - x1 + x2           x1^2 - x1 + x2]
  [1   0   1            x1*x2   0   1   0         -x1 + x2                 x1*x2         -x1^2 + x1*x2                     x2^2]
  [0   0   0                0   1   1   1   x1^2 - x1 + x2   x1^3 - x1^2 + x1*x2   x1^3 - x1^2 + x1*x2   x1^2*x2 - x1*x2 + x2^2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 + x2 - 1, x1^3 - 2*x1^2*x2 - x1^2 + 2*x1*x2 - x2^2, x1, x2, x1 - x2, x2 - 1, x1^2 - x1*x2 + x2^2, x1^2 - 2*x1*x2 + x2, x1^2*x2 - x1^2 + x1*x2 - x2^2, x1^2 - x1 + x2, x1 - 1, x1*x2 - x1 + x2, x1^2*x2 - x1^2 - x1*x2 + x1 + 2*x2^2 - x2, x1^3 - 3*x1^2 + 2*x1*x2 + x1 - x2, 2*x1^2 - x1*x2 - x1 + x2, x1^2 - x1*x2 + x2, x1^3 - 2*x1^2 + 2*x1*x2 + x1 - x2, x1^2 - 2*x1 + 2*x2]