The realization space is
  [1   1   0   0        1    1   0   x1^2 + x1 - 1   x1^2 + x1 - 1       x1^2 + x1 - 1    x1^3 + 2*x1^2 - 1]
  [1   0   1   1   x1 + 1   x1   0   x1^2 + x1 - 1               0   x1^3 + 2*x1^2 - 1   x1^4 + 2*x1^3 - x1]
  [1   0   1   0        1    0   1          x1 - 1              -1                  -1                  -x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^13 - 4*x1^12 - x1^11 + 11*x1^10 + 6*x1^9 - 12*x1^8 - 5*x1^7 + 6*x1^6 + x1^5 - x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 + 2, x1 + 1, x1^2 + x1 + 1, x1^4 + 2*x1^3 - x1 - 1, x1^3 + x1^2 - 1, x1 - 1, x1^2 + x1 - 1, x1^3 + 2*x1^2 + x1 - 1]