The realization space is
  [1   1   0          1   0   1   1        0                  x1         1    1]
  [0   1   1   2*x1 - 1   0   0   1   x1 - 1         2*x1^2 - x1   -x1 + 1   x1]
  [0   0   0          0   1   1   1      -x1   2*x1^2 - 2*x1 + 1        x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-8*x1^5 + 21*x1^4 - 21*x1^3 + 10*x1^2 - 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2*x1^2 - 2*x1 + 1, 2, 4*x1^3 - 5*x1^2 + 3*x1 - 1, 3*x1 - 2, 4*x1 - 3, x1 - 2, 4*x1^2 - 2*x1 + 1, 4*x1^2 - 3*x1 + 1]