The realization space is
  [1   0   1   2*x1 - 1   1   0    1   1         1                 0    1]
  [0   1   1       x1^2   0   0    0   1        x1   x1^2 - 2*x1 + 1   x1]
  [0   0   0          0   1   1   x1   1   -x1 + 1         -2*x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^10 - 11*x1^9 + 21*x1^8 - 10*x1^7 - 21*x1^6 + 37*x1^5 - 25*x1^4 + 8*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1^2 + x1 - 1, x1^3 - x1^2 + 2*x1 - 1, x1 - 1, x1^3 - 5*x1^2 + 4*x1 - 1, x1^2 - 4*x1 + 2, x1^2 - 3*x1 + 1, x1^3 - 2*x1^2 - x1 + 1]