The realization space is
  [1   1   x1 - 1   0   0   1   -2*x1^2 + 2*x1 - 1    1      x1 - 1    0        x1^2 - x1]
  [0   1       -1   1   0   0                    0    1          -1    1   -x1^2 + x1 - 1]
  [0   0        0   0   1   1           -x1^2 + x1   x1   x1^2 - x1   x1        x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-3*x1^12 + 14*x1^11 - 31*x1^10 + 42*x1^9 - 37*x1^8 + 21*x1^7 - 7*x1^6 + x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1^2 - x1 + 1, x1 - 1, 2*x1^2 - 2*x1 + 1, x1 + 1, 2*x1^2 - 3*x1 + 2, x1 - 2]