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