The realization space is
  [1   0   1    1   1   0   2*x1 - 1   1         1        0    1]
  [0   1   1   x1   0   0          0   1   -x1 + 1   x1 - 1   x1]
  [0   0   0    0   1   1       x1^2   1        x1       -1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^6 + 12*x1^5 - 13*x1^4 + 6*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1 + 1, x1^2 - x1 + 1, x1 - 1, 2*x1 - 1, x1^2 + x1 - 1, x1 - 2, x1^2 - 3*x1 + 1, x1^3 - x1^2 - 2*x1 + 1]