The realization space is
  [1   0   1   x1 - 1   0   1    0    1   x1^2 - x1     1]
  [0   1   1       -1   0   0    1    1         -x1   -x1]
  [0   0   0        0   1   1   -1   x1    x1^2 - 1    x1]
in the multivariate polynomial ring in 1 variable over ZZ
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 - 1, x1, x1 + 1, x1 - 1, 2*x1^2 - 1, x1^3 - x1^2 + 1]