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