The realization space is
  [1   1    1    1   0      1   0   x1^2   x1^2      1    1]
  [1   0   x1   x1   1   x1^2   0   x1^2      0   x1^2   x2]
  [1   0   x1    1   0     x1   1     x3     x3     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[x1^2 - x2, x3 - 1, x3, x1 - x3, x1 + 1, x1 - 1, x1^2*x2 - x1^2*x3 - x2*x3 + x3, x2, x1^3*x2 - x1^3*x3 + x1*x3 - x2*x3, x1^3*x3 - x1^2*x2 - x1*x3 + x2*x3, x1^4*x3 - x1^3*x2 - x1^2*x3 + x2*x3, x1^2 - x3, x2 - 1, x1^3*x2 - x1^3*x3 - x1^3 + x1^2*x3 + x1*x3 - x2*x3, x1^3*x3 - x1^2*x2 - x1^2*x3 + x1^2 - x1*x3 + x2*x3, x1^4*x3 - x1^3*x2 + x1^3 - 2*x1^2*x3 + x2*x3, x1 - x2, x1*x3 - x1 - x2 + x3, x1*x3 - x2, x1, x2 - x3, x1^4 - 2*x1^2*x3 + x3, x1^4 - x1^2*x3 - x1*x3 + x3, x1^3 - x1^2*x3 - x1*x3 + x3, x1^3 - x3, x1^3 - x1*x3 - x3]