The realization space is
  [1   1   0   0   1   1              0                 x1 - 2        x1 - 2          x1^3 - 3*x1^2 + x1 + 2        x1^3 - 3*x1^2 + x1 + 2]
  [1   0   1   0   1   0              1                     -1            -1                         -x1 + 1                       -x1 + 1]
  [0   0   0   1   1   1   -x1^2 + 2*x1   x1^3 - 3*x1^2 + 2*x1   x1^2 - 2*x1   x1^4 - 4*x1^3 + 5*x1^2 - 2*x1   x1^4 - 3*x1^3 + x1^2 + 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^10 - 12*x1^9 + 60*x1^8 - 158*x1^7 + 221*x1^6 - 121*x1^5 - 64*x1^4 + 104*x1^3 - 16*x1^2 - 16*x1)
avoiding the zero loci of the polynomials
RingElem[x1^3 - 3*x1^2 + 2*x1 + 1, x1, x1 - 2, x1 - 1, x1^2 - 2*x1 - 1, x1^2 - x1 - 1, x1^4 - 4*x1^3 + 4*x1^2 + x1 - 1, x1^4 - 3*x1^3 + x1^2 + 3*x1 - 1, x1^3 - 4*x1^2 + 3*x1 + 1, x1^4 - 5*x1^3 + 8*x1^2 - 4*x1 - 1, x1^2 - 3*x1 + 1]