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