The realization space is
  [1   0   1          1   0   1    0         x1          1         x1         x1]
  [0   1   1   2*x1 - 1   0   0    1         x1   2*x1 - 1   2*x1 - 1   2*x1 - 1]
  [0   0   0          0   1   1   -1   2*x1 - 1         x1         x1   2*x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (8*x1^5 - 28*x1^4 + 38*x1^3 - 25*x1^2 + 8*x1 - 1)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1 - 1, 3*x1 - 2, x1, 2, x1 - 2, 3*x1 - 1, 2*x1^2 - 4*x1 + 1, 2*x1^2 - 2*x1 + 1]