The realization space is
  [1   1   0                 x1   0   1   1         0                 x1         1    1]
  [0   1   1   -x1^2 + 3*x1 - 1   0   0   1        x1   -x1^2 + 3*x1 - 1        x1   x1]
  [0   0   0                  0   1   1   1   -x1 + 1               x1^2   -x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^8 + 16*x1^7 - 55*x1^6 + 104*x1^5 - 118*x1^4 + 83*x1^3 - 36*x1^2 + 9*x1 - 1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2*x1^2 - 2*x1 + 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1, 2, x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1^2 - 3*x1 + 1, 3*x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^3 - 3*x1^2 + 4*x1 - 1]