The realization space is
  [1   0   1   1   0   1         1         0         1                x1]
  [0   1   1   0   0   1        x1        x1   -x1 + 1              x1^2]
  [0   0   0   1   1   1   -x1 + 1   -x1 + 1   -x1 + 1   x1^2 - 2*x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-8*x1^7 + 20*x1^6 - 18*x1^5 + 7*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, 2*x1 - 1, x1, 2, 2*x1^2 - 4*x1 + 1, x1 - 2, x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1]