The realization space is
  [1   0   1           x1 - 1   1   0         1         1        0    1]
  [0   1   1   -x1^2 + x1 - 1   0   0   -x1 + 1   -x1 + 1   x1 - 1    1]
  [0   0   0                0   1   1         1        x1       -1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^8 - 5*x1^7 + 13*x1^6 - 20*x1^5 + 18*x1^4 - 9*x1^3 + 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + 1, x1, x1^2 - 2*x1 + 2, x1 - 1, x1 - 2, 2*x1^2 - 3*x1 + 2]