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