The realization space is
  [1   0   1        2*x1 - 1   1   0          x1 - 1   1         1           0    1]
  [0   1   1   x1^2 + x1 - 1   0   0               0   1        x1   x1^2 - x1   x1]
  [0   0   0               0   1   1   x1^2 + x1 - 1   1   -x1 + 1   -2*x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^11 + 12*x1^10 + 3*x1^9 - 42*x1^8 + 39*x1^7 + 16*x1^6 - 47*x1^5 + 31*x1^4 - 9*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1^2 + x1 - 1, x1, 2*x1 - 1, x1^2 + 2*x1 - 1, x1 - 1, x1^3 + 2*x1^2 - 3*x1 + 1, x1^2 - 4*x1 + 2, x1^2 - 3*x1 + 1]