The realization space is
  [1    1   1   0   0   1    1         x1                  0                 x1              2*x1 - 1]
  [1   x1   0   1   0   1   x1          0   -x1^2 + 2*x1 - 1   -x1^2 + 3*x1 - 1   -x1^3 + 3*x1^2 - x1]
  [0    0   0   0   1   1   x1   2*x1 - 1           2*x1 - 1           2*x1 - 1           2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^13 + 20*x1^12 - 25*x1^11 - 4*x1^10 + 30*x1^9 - 24*x1^8 + 8*x1^7 - x1^6)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, 2*x1 - 1, x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, x1^3 - 4*x1^2 + 3*x1 - 1, x1^2 + x1 - 1, x1^4 - 2*x1^3 + 5*x1^2 - 4*x1 + 1, 3*x1^2 - 3*x1 + 1]