The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1        0   x1^2 - 2*x1 + 1    1              x1]
  [1   0   1             -x1^2   0   1   0       x1             -x1^2   x1            x1^2]
  [0   0   0                 0   1   1   1   x1 - 1    -x1^2 + x1 - 1   x1   x1^2 - x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^10 + 20*x1^9 - 54*x1^8 + 98*x1^7 - 128*x1^6 + 123*x1^5 - 86*x1^4 + 42*x1^3 - 13*x1^2 + 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, x1^3 - x1 + 1, x1^3 - x1^2 + 1, x1^2 - 2*x1 + 2, 2*x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, 3*x1^2 - 3*x1 + 2, 2*x1^2 - 3*x1 + 2]