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