The realization space is
  [1   0   1    1   1   0   -x1 + 1   1               1                0            1]
  [0   1   1   x1   0   0         0   1   x1^2 - x1 + 1   -x1^2 + x1 - 1           x1]
  [0   0   0    0   1   1     -x1^2   1      -x1^2 + x1        x1^2 - x1   -x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^10 + 5*x1^9 - 14*x1^8 + 26*x1^7 - 33*x1^6 + 29*x1^5 - 17*x1^4 + 6*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - 2*x1 + 2, x1^4 - 3*x1^3 + 4*x1^2 - 2*x1 + 1, x1^4 - 3*x1^3 + 5*x1^2 - 3*x1 + 1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^3 - 2*x1^2 + x1 - 1]