The realization space is
  [1   1   0                x1   0   1   1        0                x1         1         1]
  [1   0   1   x1^2 - 2*x1 + 1   0   1   0   x1 - 1   x1^2 - 2*x1 + 1   -x1 + 1   -x1 + 1]
  [0   0   0                 0   1   1   1       x1        -x1^2 + x1   -x1 + 1        x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^10 + 15*x1^9 - 45*x1^8 + 71*x1^7 - 64*x1^6 + 33*x1^5 - 9*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2, 3*x1 - 1, 2*x1^2 - 2*x1 + 1, x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, x1 - 2, 2*x1^2 - 4*x1 + 1]