The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1        0   x1^2 - 2*x1 + 1   x1 - 1      x1 - 1]
  [1   0   1                x1   0   1   0       x1                x1      -x1         -x1]
  [0   0   0                 0   1   1   1   x1 - 1        -x1^2 + x1      -x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^8 + 14*x1^7 - 28*x1^6 + 23*x1^5 - 8*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 + 1, x1 - 1, x1^2 + 2*x1 - 1, x1^2 + x1 - 1, x1^2 - 3*x1 + 1, 3*x1 - 1, 2, 2*x1^2 - 4*x1 + 1]