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