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