The realization space is
  [1    1   1   0   0   1    1   x1^2 - 2*x1 + 1        0   x1^2 - 2*x1 + 1                 x1]
  [1   x1   0   1   0   1   x1                 0   x1 - 1        -x1^2 + x1   -x1^2 + 3*x1 - 1]
  [0    0   0   0   1   1   x1              x1^2      -x1              x1^2               x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^10 - 14*x1^9 + 40*x1^8 - 61*x1^7 + 54*x1^6 - 28*x1^5 + 8*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 - 1, x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1 - 1, x1 - 2, 2*x1^2 - 4*x1 + 1, 2]