The realization space is
  [1   1   0   0        1    1   0          x1 + 1   x1 + 1            x1 + 1             x1 + 1]
  [1   0   1   1   x1 + 1   x1   0          x1 + 1        0   x1^2 + 2*x1 + 1          x1^2 + x1]
  [0   0   0   1       x1   x1   1   x1^2 + x1 + 1     x1^2     x1^2 + x1 + 1   x1^3 + 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 - 10*x1^8 - 9*x1^7 - x1^6 + 6*x1^5 + 8*x1^4 + 7*x1^3 + 4*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1^2 + x1 + 1, x1^2 - x1 + 1, x1, x1 - 1, x1^2 + 1, 2*x1^2 + 1, x1^3 + x1^2 + 1, x1^3 + x1 + 1, x1 + 1]