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 (-2*x1^7 + 6*x1^6 - 8*x1^5 + 8*x1^4 - 7*x1^3 + 4*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, 2*x1^2 - 2*x1 + 1, 2, 2*x1^3 - 2*x1^2 + 2*x1 - 1, 2*x1 - 1, x1, x1^2 - x1 + 1]