The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1                   0   x1^2 - 2*x1 + 1    1        x1 - 1]
  [1   0   1      -2*x1^2 + x1   0   1   0   2*x1^2 - 2*x1 + 1      -2*x1^2 + x1   x1   2*x1^2 - x1]
  [0   0   0                 0   1   1   1           x1^2 - x1        -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 (-6*x1^10 + 48*x1^9 - 137*x1^8 + 209*x1^7 - 196*x1^6 + 118*x1^5 - 45*x1^4 + 10*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 - 1, 3*x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, x1^2 - x1 + 1, x1^3 - 4*x1^2 + 3*x1 - 1, x1^3 + x1^2 - 2*x1 + 1]