The realization space is
  [1   1   0    1   0   1   1    0           1           1           1]
  [1   0   1   -1   0   1   0    1          -1   -3*x1 + 1   -3*x1 + 1]
  [0   0   0    0   1   1   1   x1   -3*x1 + 1   -3*x1 + 1   -3*x1 + 2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (3*x1^2 - 3*x1 + 1, 243*x1^5 - 486*x1^4 + 297*x1^3 - 54*x1^2)
avoiding the zero loci of the polynomials
RingElem[3, x1, 3*x1 - 1, 3*x1 - 2, 9*x1^2 - 9*x1 + 4, 9*x1^2 - 6*x1 + 2, 3*x1^2 - 2*x1 + 1, 3*x1^2 - 3*x1 + 2, 3*x1^2 - 4*x1 + 2, x1 - 1, 2, 3*x1^2 - 5*x1 + 1, 3*x1 - 4, 6*x1 - 1, 2*x1 - 1, 3*x1 + 1, x1 + 1]