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   2*x1 - 1   -x1^2 + 3*x1 - 1        x1   x1]
  [0   0   0                  0   1   1   1        -x1               x1^2   -x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-8*x1^11 + 40*x1^10 - 86*x1^9 + 104*x1^8 - 77*x1^7 + 35*x1^6 - 9*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 3*x1 - 1, 3*x1 - 2, 3*x1^2 - 3*x1 + 1, x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, x1^2 + 2*x1 - 1, x1^2 + x1 - 1]