The realization space is
  [1   1   0   -x1^2 + x1 - 1   0   1   1         0      -x1^2 + x1 - 1    1            1]
  [1   0   1              -x1   0   1   0       -x1                 -x1   x1           x1]
  [0   0   0                0   1   1   1   -x1 + 1   -x1^3 + x1^2 - x1   x1   -x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^12 + 3*x1^11 - 3*x1^10 - x1^9 + 5*x1^8 - 4*x1^7 + x1^6)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^3 - x1 + 1, x1^2 + x1 - 1, x1 + 1, x1^2 - x1 + 1, 2*x1 - 1, x1^4 - 2*x1^2 + 3*x1 - 1, x1^3 - x1^2 + 1, x1^3 - 2*x1^2 + 3*x1 - 1, 2*x1^2 - 2*x1 + 1]