The realization space is
  [1   0   1   0   1   0        1                          1                  1                  1                          1]
  [1   1   0   1   0   0   x1 - 1   x1^3 - 3*x1^2 + 3*x1 - 1   -x1^2 + 2*x1 - 1   -x1^2 + 2*x1 - 1   x1^3 - 3*x1^2 + 3*x1 - 1]
  [1   1   0   0   1   1        0                 -x1^2 + x1         -x1^2 + x1                 x1                         x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 1 generator
avoiding the zero loci of the polynomials
RingElem[x1^4 - 4*x1^3 + x1^2*x2 + 5*x1^2 - 2*x1*x2 - 3*x1 + 2*x2, x1 - 1, x1^3 - 2*x1^2 + 2*x1 - x2, x1^2 - x1 + x2, x1 - x2, x1^2 - 2*x1 + x2, x1, x1^5 - 4*x1^4 + 7*x1^3 - x1^2*x2 - 7*x1^2 + 2*x1*x2 + 3*x1 - 2*x2, x1^3 - 3*x1^2 + 2*x1 - x2, x1^3 - 2*x1^2 + x1 - x2, x1^2 - x1 + 1, x1 - 2, x2, x2 - 1, x1^3 - 3*x1^2 + 3*x1 - x2, x1^3 - 3*x1^2 + 3*x1 - x2 - 1, x1^2 - 2*x1 + 2]