The realization space is
  [1   1   0   0      x3           x3   0                     x3                     x3      x3    1]
  [0   1   1   1   x1*x2   x1*x2 + x3   0                      0                     x3   x1*x2   x2]
  [0   1   1   0       0           x3   1   x1^2*x2 - x1*x2 + x3   x1^2*x2 - x1*x2 + x3   x1*x3   x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal with 3 generators
avoiding the zero loci of the polynomials
RingElem[x1 - x3, x2 - x3, x2, x1, x1*x2 - x2 + x3, x1^2*x2 - x1*x2 + x3, x1*x2 - x3, x2 - 1, x1 - 1, x1^2*x2 - x1*x2 + x2*x3 - x3^2, x1^2*x2 - x1*x2 - x3^2 + x3, x1^2*x2^2 - x1^2*x2 - x1*x2^2 + x1*x2 + x3^2 - x3, x1^2*x2 - x1*x2 + x2*x3 - x3^2 + x3, x1^3*x2 - x1^2*x2*x3 - x1^2*x2 + x1*x2*x3 - x1*x3^2 + x1*x3 - x3^2, x1^3*x2^2 - x1^2*x2^2*x3 - x1^2*x2^2 + x1^2*x2*x3 + x1*x2^2*x3 - x1*x2*x3^2 - x3^3 + x3^2, x1*x2 - x2*x3 + x3, x3 - 1, x1*x2 - x2*x3 + x3^2, x3, x1*x2*x3 - x1*x2 + x2*x3 - x3^2, x1^2*x2^2 - x1*x2*x3 + x3^2, x1^2*x2 - x1*x3 + x3, x1*x2 + x3, x1^2*x2 + x3, x1^3*x2^2 - x1^2*x2^2 - x1^2*x2*x3 + x1*x2*x3 - x3^2]