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