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