The realization space is
  [1   1   0                x1   0   1   1          0                  2*x1^2 - x1                         x1^2                  x1]
  [1   0   1   x1^2 - 2*x1 + 1   0   1   0   2*x1 - 1   2*x1^3 - 5*x1^2 + 4*x1 - 1   2*x1^3 - 5*x1^2 + 4*x1 - 1   2*x1^2 - 3*x1 + 1]
  [0   0   0                 0   1   1   1         x1                  x1^3 - x1^2           x1^3 - 2*x1^2 + x1                x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (32*x1^14 - 200*x1^13 + 508*x1^12 - 694*x1^11 + 563*x1^10 - 280*x1^9 + 84*x1^8 - 14*x1^7 + x1^6)
avoiding the zero loci of the polynomials
RingElem[x1^2 - 3*x1 + 1, 2*x1 - 1, x1 - 1, x1, x1 - 2, 3*x1 - 1, 2*x1^2 - 4*x1 + 1, 3*x1^3 - 8*x1^2 + 5*x1 - 1, 2*x1^3 - 6*x1^2 + 4*x1 - 1]