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