The realization space is
  [1   1   0            x1^2 - x1   0   1   1          0            x1^2 - x1   x1 - 1                  x1]
  [1   0   1   -2*x1^2 + 2*x1 - 1   0   1   0   2*x1 - 1   -2*x1^2 + 2*x1 - 1      -x1   2*x1^2 - 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 (12*x1^12 - 68*x1^11 + 170*x1^10 - 246*x1^9 + 226*x1^8 - 135*x1^7 + 51*x1^6 - 11*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, 3*x1^2 - 3*x1 + 1, 3*x1 - 1, 2, 4*x1^2 - 3*x1 + 1]