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