The realization space is
  [1   1   x1^2 - x1 + 1   0   0   1   -x1^2 + 2*x1 - 1   x1^3 - 2*x1^2 + 2*x1 - 1    0   x1 - 1    1]
  [1   0              x1   1   0   1                  0                  x1^2 - x1   x1       -1   x1]
  [0   0               0   0   1   1                 x1             -x1^2 + x1 - 1    1       -1    1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^8 - 9*x1^7 + 19*x1^6 - 23*x1^5 + 16*x1^4 - 6*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, 2*x1 - 1, x1^4 - 2*x1^3 + 4*x1^2 - 3*x1 + 1, x1^3 - 2*x1^2 + 3*x1 - 1]