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