The realization space is
  [1   x1 - 1   1   0   0   1   x1 - 1      1           0          x1 - 1      2*x1 - 1]
  [1      -x1   0   1   0   1      -x1      0           1           -2*x1           -x1]
  [0        0   0   0   1   1      -x1   2*x1   -2*x1 + 1   2*x1^2 - 2*x1   2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-8*x1^6 + 22*x1^5 - 18*x1^4 + 4*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 1, 2, 4*x1 - 1, 2*x1 - 1, x1 - 1, 4*x1^2 - 3*x1 + 1, 4*x1 - 3]