The realization space is
  [1   1                   1   0   0   1    1                   1                   0                   1                   1]
  [1   0   4*x1^2 - 4*x1 + 1   1   0   1    0   4*x1^2 - 4*x1 + 1                   1   2*x1^2 - 2*x1 + 1   2*x1^2 - 2*x1 + 1]
  [0   0                   0   0   1   1   x1   2*x1^2 - 2*x1 + 1   2*x1^2 - 4*x1 + 2   2*x1^2 - 2*x1 + 1                  x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^3 - 8*x1^2 + 4*x1 - 1)
avoiding the zero loci of the polynomials
RingElem[x1, 2, x1 - 1, 2*x1 - 1, 2*x1^2 - 2*x1 + 1, 4*x1^3 - 12*x1^2 + 12*x1 - 5, 4*x1^4 - 12*x1^3 + 14*x1^2 - 9*x1 + 2, 4*x1^3 - 12*x1^2 + 12*x1 - 3, 4*x1^3 - 8*x1^2 + 2*x1 + 1, 2*x1^2 - 4*x1 + 1, 4*x1^4 - 12*x1^3 + 10*x1^2 - 2*x1 - 1, 4*x1^4 - 12*x1^3 + 14*x1^2 - 6*x1 + 1, 2*x1^3 - 2*x1 + 1, 8*x1^4 - 18*x1^3 + 16*x1^2 - 6*x1 + 1, 8*x1^4 - 24*x1^3 + 22*x1^2 - 6*x1 - 1, 8*x1^4 - 24*x1^3 + 24*x1^2 - 10*x1 + 1, 2*x1 - 3, 4*x1^2 - 6*x1 + 1, 2*x1^2 - 3*x1 + 2, 8*x1^4 - 24*x1^3 + 26*x1^2 - 11*x1 + 2, 8*x1^4 - 24*x1^3 + 24*x1^2 - 8*x1 + 1, 2*x1^2 - 1]