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