The realization space is
  [1   1   0   x1 - 1   0   1   1          0   x1 - 1   x1 - 1      1]
  [1   0   1    -2*x1   0   1   0   2*x1 - 1    -2*x1      -x1   2*x1]
  [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 (18*x1^8 - 51*x1^7 + 57*x1^6 - 32*x1^5 + 9*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 1, 2*x1 - 1, 2, x1 - 1, 3*x1 - 2, 3*x1^2 - 3*x1 + 1, x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, 4*x1 - 1]