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         1                 -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 (x1^10 - 5*x1^9 + 11*x1^8 - 14*x1^7 + 11*x1^6 - 5*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - x1 + 1, x1^3 - x1^2 + 1, x1 + 1, 2*x1 - 1, 2*x1^2 - 2*x1 + 1, x1^2 + 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1 - 2, x1^2 - 2*x1 + 2]