The realization space is
  [1   0   1         1   1   0   1         1               1               1]
  [0   1   1   -x1 + 1   0   0   1   -x1 + 1   x1^2 - x1 + 1   x1^2 - x1 + 1]
  [0   0   0         0   1   1   1        x1   x1^2 - x1 + 1              x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^11 + 11*x1^10 - 28*x1^9 + 44*x1^8 - 47*x1^7 + 35*x1^6 - 18*x1^5 + 6*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + 1, x1 - 1, x1, 2*x1 - 1, 2*x1^2 - 2*x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1]