The realization space is
  [1   0   1   1   0   1                                 2*x2^2 - x2                          x2^2                                          2*x2^3 - x2^2                              2*x2^2 - x2    1]
  [0   1   1   0   0   1      x1*x2^2 - 2*x1*x2 + x1 + x2^2 + x2 - 1   -x1*x2 + x1 + x2^2 + x2 - 1   -2*x1*x2^2 + 3*x1*x2 - x1 + 2*x2^3 + x2^2 - 3*x2 + 1   x1*x2^2 - 2*x1*x2 + x1 + x2^2 + x2 - 1   x1]
  [0   0   0   1   1   1   -x1*x2^2 + 2*x1*x2 - x1 + x2^2 - 2*x2 + 1                    -x2^2 + x2      -x1*x2^3 + 2*x1*x2^2 - x1*x2 + x2^3 - 2*x2^2 + x2                            2*x2^3 - x2^2   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 - 1, x2^2 + x2 - 1, x2, x2 - 1, x1*x2^2 - 2*x1*x2 + x1 + 2*x2^3 - 2*x2^2 + 2*x2 - 1, x1*x2 - x1 - 3*x2 + 2, x1^2*x2^3 - 2*x1^2*x2^2 + x1^2*x2 - x1*x2^3 + 6*x1*x2^2 - 5*x1*x2 + x1 + 2*x2^4 - x2^3 - 4*x2^2 + 4*x2 - 1, 2*x2 - 1, x1*x2^3 - 2*x1*x2^2 + x1*x2 - x2^3 + 6*x2^2 - 5*x2 + 1, x1 + x2 - 1, x1^2*x2^2 - 2*x1^2*x2 + x1^2 + x1*x2^3 - 3*x1*x2^2 + 3*x1*x2 - x1 + x2^3 + x2^2 - x2, x1*x2^2 - 2*x1*x2 + x1 + x2^2 + x2 - 1, x1*x2^2 - 2*x1*x2 + x1 + x2^3 - 2*x2^2 + 4*x2 - 2, x1 - x2, x1, x1^2*x2^4 - 4*x1^2*x2^3 + 6*x1^2*x2^2 - 4*x1^2*x2 + x1^2 - 4*x1*x2^4 + 11*x1*x2^3 - 13*x1*x2^2 + 8*x1*x2 - 2*x1 + 4*x2^5 - x2^4 - 6*x2^3 + 7*x2^2 - 4*x2 + 1, x1*x2^3 - 3*x1*x2^2 + 3*x1*x2 - x1 - 5*x2^3 + 7*x2^2 - 4*x2 + 1, x1^2*x2^4 - 4*x1^2*x2^3 + 6*x1^2*x2^2 - 4*x1^2*x2 + x1^2 - 2*x1*x2^4 + 10*x1*x2^3 - 17*x1*x2^2 + 12*x1*x2 - 3*x1 + 4*x2^5 - 3*x2^4 - 5*x2^3 + 11*x2^2 - 8*x2 + 2, x1*x2 - x1 - 2*x2^2 + 1, x1*x2 - x1 - x2^2 - x2 + 1, x1*x2^3 - 4*x1*x2^2 + 4*x1*x2 - x1 + x2^3 + 3*x2^2 - 4*x2 + 1, 2*x1*x2^2 - 4*x1*x2 + 2*x1 + 3*x2 - 2]