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