The realization space is
  [1   1   0        x1^2 - x1   0   1   1        0        x1^2 - x1    1              x1]
  [1   0   1   -x1^2 + x1 - 1   0   1   0   x1 - 1   -x1^2 + x1 - 1   x1   x1^2 - x1 + 1]
  [0   0   0                0   1   1   1       x1            -x1^2   x1            x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^13 + 18*x1^12 - 38*x1^11 + 51*x1^10 - 49*x1^9 + 35*x1^8 - 18*x1^7 + 6*x1^6 - x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, x1^3 - x1 + 1, x1^3 + x1^2 - 2*x1 + 1, 2*x1 - 1, x1 - 2, 3*x1^2 - 2*x1 + 1]