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 (-2*x1^10 + 11*x1^9 - 30*x1^8 + 51*x1^7 - 58*x1^6 + 45*x1^5 - 23*x1^4 + 7*x1^3 - x1^2)
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]