The realization space is
  [1   1   0   0   x1 - 1      x1 - 1   0         1         1      x1 - 1      x1 - 1]
  [1   0   1   1      -x1   -2*x1 + 1   0         1         0         -x1   -2*x1 + 1]
  [1   0   1   0   x1 - 1           0   1   -x1 + 1   -x1 + 1   x1^2 - x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (12*x1^8 - 44*x1^7 + 63*x1^6 - 44*x1^5 + 15*x1^4 - 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, 2*x1 - 1, 3*x1 - 2, 2*x1^2 - 1, x1^2 + x1 - 1, 3*x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1]