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