The realization space is
  [1   0   1            1   0   1    0       x1            1                 x1                 x1]
  [0   1   1   -x1^2 + x1   0   0    1       x1   -x1^2 + x1   -x1^2 + 2*x1 - 1   -x1^2 + 2*x1 - 1]
  [0   0   0            0   1   1   -1   x1 - 1           x1             x1 - 1               x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^10 - 6*x1^9 + 18*x1^8 - 36*x1^7 + 53*x1^6 - 60*x1^5 + 53*x1^4 - 36*x1^3 + 18*x1^2 - 6*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + 1, x1 - 1, x1, 2*x1 - 1, x1^3 - x1^2 + 2*x1 - 1, x1^2 + 1, x1 - 2, x1^2 - 2*x1 + 2, x1^2 - x1 + 2]