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