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