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