The realization space is
  [1   0   1         1   1   0   1         1    1         x1]
  [0   1   1   -x1 + 1   0   0   1   -x1 + 1   x1       x1^2]
  [0   0   0         0   1   1   1        x1   x1   2*x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^5 + 6*x1^4 - 9*x1^3 + 5*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 - 1, x1^3 + 2*x1^2 - 3*x1 + 1, x1^2 + x1 - 1, x1^2 - 3*x1 + 1]