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 + 34*x1^7 - 43*x1^6 + 37*x1^5 - 21*x1^4 + 7*x1^3 - x1^2)
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]