The realization space is
  [1   1   0   2*x1^2 - 2*x1 + 1   0   1   1        0   4*x1^3 - 6*x1^2 + 4*x1 - 1   2*x1 - 1    1]
  [0   1   1                  x1   0   0   1       x1                  2*x1^2 - x1         x1   x1]
  [0   0   0                   0   1   1   1   x1 - 1   2*x1^3 - 4*x1^2 + 3*x1 - 1     x1 - 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-16*x1^10 + 104*x1^9 - 288*x1^8 + 444*x1^7 - 418*x1^6 + 248*x1^5 - 92*x1^4 + 20*x1^3 - 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 - 1, 2*x1^2 - 2*x1 + 1, 2, 2*x1^3 - 6*x1^2 + 4*x1 - 1, 6*x1^3 - 8*x1^2 + 4*x1 - 1, 2*x1^3 - 2*x1 + 1, 6*x1^3 - 10*x1^2 + 6*x1 - 1, 2*x1^4 - 10*x1^3 + 12*x1^2 - 6*x1 + 1, 3*x1^2 - 3*x1 + 1]