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