The realization space is
  [1   1   0   x1 - 1   0   1   1         0   x1 - 1         1     1]
  [0   1   1     2*x1   0   0   1        x1     2*x1   -x1 + 1   -x1]
  [0   0   0        0   1   1   1   -x1 + 1    -2*x1        x1    x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^4 + 2*x1^2 - 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1 + 1, 2, x1^2 + 1, 2*x1^2 - x1 + 1, 2*x1 - 1, 3*x1 - 1]