The realization space is
  [0   1   1   0   0   1   x1   x1^3 - x1^2 - x1   x1^3 - x1^2 - x1     x1     x1^3 - x1^2 - x1]
  [1   1   0   1   0   0    1            -x1 - 1                 -1      1                   -1]
  [1   1   0   0   1   1    0              -x1^2              -x1^2   x1^2   x1^4 - x1^3 - x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^11 + 2*x1^10 - 2*x1^8 + x1^6)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1 + 1, x1^3 - x1^2 - 1, x1^4 - x1^3 - 1, x1^2 - 2, x1^2 - x1 - 1, x1 - 2, x1^4 - 2*x1^3 + x1 + 1, x1^3 - x1 - 1, x1^3 - x1^2 + 1]