The realization space is
  [1   1   0           x1 + 1   0   1   x1 + 1        0   x1 + 1   x1^3 + 2*x1^2 - 1      x1 + 1]
  [1   0   1   -x1^3 - 2*x1^2   0   1        0   x1 + 1       x1       x1^3 + 2*x1^2          x1]
  [0   0   0                0   1   1       x1        1       x1         x1^3 + x1^2   x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^12 + 7*x1^11 + 19*x1^10 + 24*x1^9 + 11*x1^8 - 5*x1^7 - 7*x1^6 - 2*x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, x1 + 1, x1 - 1, x1^3 + 2*x1^2 + x1 + 1, x1 + 2, x1^2 + x1 - 1, x1^2 + x1 + 1]