The realization space is
  [1   1   0   2*x1^2 - 2*x1 + 1   0   1   1        0      2*x1^2 - 2*x1 + 1   2*x1 - 1    1]
  [0   1   1                  x1   0   0   1       x1                     x1         x1   x1]
  [0   0   0                   0   1   1   1   x1 - 1   2*x1^3 - 2*x1^2 + x1     x1 - 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-8*x1^9 + 32*x1^8 - 52*x1^7 + 42*x1^6 - 16*x1^5 + 2*x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2*x1 - 1, 2*x1^2 - 2*x1 + 1, 2, 2*x1^3 - 2*x1^2 + 1, 2*x1^3 - 4*x1^2 + 4*x1 - 1, 2*x1^3 - 2*x1^2 + 2*x1 - 1, 2*x1^4 - 4*x1^2 + 4*x1 - 1, 2*x1^3 - 2*x1 + 1, 3*x1^2 - 3*x1 + 1]