The realization space is
  [1   1   0            x1^2   0   1   1                        0               x1^2                x1^2                x1^2]
  [0   1   1   x1^2 - x1 + 1   0   0   1                     x1^2      x1^2 - x1 + 1   2*x1^2 - 2*x1 + 1   2*x1^2 - 2*x1 + 1]
  [0   0   0               0   1   1   1   x1^3 + x1^2 - 2*x1 + 1   -x1^2 + 2*x1 - 1    -x1^2 + 2*x1 - 1                x1^3]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1^3 + x1^2 - 2*x1 + 1, 2*x1^2 - 2*x1 + 1, x1 - 1, 3*x1^2 - 3*x1 + 1, x1^5 + 2*x1^4 - 6*x1^3 + 7*x1^2 - 4*x1 + 1, x1^3 + 2*x1^2 - 2*x1 + 1, x1^4 + 3*x1^3 - 6*x1^2 + 4*x1 - 1, x1^2 - x1 + 1, x1, 2*x1^5 + x1^4 - 7*x1^3 + 8*x1^2 - 4*x1 + 1, x1^3 + 2*x1^2 - 3*x1 + 1, 3*x1^2 - 4*x1 + 2, x1^5 + x1^4 - 4*x1^3 + 5*x1^2 - 3*x1 + 1, x1^5 + 2*x1^4 - 4*x1^3 + 5*x1^2 - 3*x1 + 1, x1^4 - 2*x1^3 + 4*x1^2 - 3*x1 + 1, 2*x1^2 - 3*x1 + 2, x1^2 + x1 - 1, x1^5 + x1^4 - 2*x1^3 + 4*x1^2 - 3*x1 + 1]