The realization space is
  [1   0   1   0   1    0                               x1*x2                          x1                               x1*x2          x2          x1]
  [0   1   1   0   0    1                               x1*x2   -x1^2 + x1*x2 + 2*x1 - x2                      2*x1*x2 - x2^2   2*x1 - x2   2*x1 - x2]
  [0   0   0   1   1   -1   x1^2*x2 + 2*x1^2 - 3*x1*x2 + x2^2                        x1^2   x1^2*x2 + 2*x1^2 - 3*x1*x2 + x2^2       x1*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 - x2, 2*x1 - x2, x1*x2 + 2*x1 - x2, 2*x1^2*x2 + 4*x1^2 - 4*x1*x2 + x2^2, x1*x2 + x1 - x2, x1*x2 + 2*x1 - 2*x2, x1^2*x2 + 2*x1^2 - 3*x1*x2 + x2^2, 2*x1^2*x2 + 4*x1^2 - 5*x1*x2 + x2^2, x2 - 1, x2, x1, x1 - 1, 2, 2*x1^2*x2 + 4*x1^2 - 6*x1*x2 + x2^2, x1^2 - 2*x1 + x2, x1^3*x2 + 2*x1^3 - 3*x1^2*x2 - 2*x1^2 + x1*x2^2 + 3*x1*x2 - x2^2, x1^2*x2 + 2*x1^2 - 4*x1*x2 + x2^2, x1^3*x2 + 2*x1^3 - 5*x1^2*x2 - 4*x1^2 + x1*x2^2 + 5*x1*x2 - x2^2, x1^2 - x1*x2 - 2*x1 + x2, x1^2*x2 + 2*x1^2 - 2*x1*x2 + x2^2]