The realization space is
  [1   1   0    x1 - 1   0   1   1        0    x1 - 1    1        1]
  [1   0   1   -x1 - 1   0   1   0       x1   -x1 - 1   x1   x1 + 1]
  [0   0   0         0   1   1   1   x1 - 1       -x1   x1       x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^7 - 8*x1^6 + 6*x1^5 - 4*x1^4 + 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1 + 1, 2, x1^2 + 1, x1^2 - x1 + 1, 2*x1 - 1, x1 - 2, 3]