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