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