The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1                  0   x1^2 - 2*x1 + 1   x1 - 1      x1 - 1]
  [1   0   1                 1   0   1   0                 x1                 1       -1          -1]
  [0   0   0                 0   1   1   1   -x1^2 + 2*x1 - 1        -x1^2 + x1       -1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^9 + 12*x1^8 - 32*x1^7 + 50*x1^6 - 50*x1^5 + 32*x1^4 - 12*x1^3 + 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - x1 + 1, x1 - 1, x1 - 2, x1^2 - 2*x1 + 2, 2*x1^2 - 2*x1 + 1, x1 + 1, 2*x1 - 3, 2*x1 - 1, x1^2 - 3*x1 + 1]