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