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