The realization space is
  [1   1   0                 x1   0   1   1         0                 x1         1    1]
  [0   1   1   -x1^2 + 3*x1 - 1   0   0   1        x1   -x1^2 + 3*x1 - 1        x1   x1]
  [0   0   0                  0   1   1   1   -x1 + 1               x1^2   -x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-14*x1^10 + 85*x1^9 - 223*x1^8 + 330*x1^7 - 301*x1^6 + 173*x1^5 - 61*x1^4 + 12*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2*x1^2 - 2*x1 + 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1, 2, x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1^2 - 3*x1 + 1, 3*x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^3 - 3*x1^2 + 4*x1 - 1]