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