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