The realization space is
  [1   0   1   x1 - 1   0   1    0   x1 - 1   x1^2 - 2*x1 + 1      -x1      x1 - 1]
  [0   1   1      -x1   0   0    1   x1 - 1        -x1^2 + x1   x1 - 1   x1^2 - x1]
  [0   0   0        0   1   1   -1    -x1^2       2*x1^2 - x1      -x1       -x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^11 - 12*x1^10 + 5*x1^9 + 22*x1^8 - 37*x1^7 + 25*x1^6 - 8*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1^2 + x1 - 1, x1, x1 - 1, 2*x1 - 1, x1^3 - x1^2 + 2*x1 - 1, x1^2 - x1 + 1, x1^3 + 2*x1^2 - 3*x1 + 1]