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