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 (-2*x1^11 + 10*x1^10 - 22*x1^9 + 28*x1^8 - 23*x1^7 + 13*x1^6 - 5*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]