The realization space is
  [1   1   0   2*x1^2 - 2*x1 + 1   0   1   1         0   2*x1^2 - 2*x1 + 1         1    1]
  [0   1   1          -x1^2 + x1   0   0   1        x1          -x1^2 + x1   -x1 + 1   x1]
  [0   0   0                   0   1   1   1   -x1 + 1                x1^2        x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-6*x1^8 + 18*x1^7 - 23*x1^6 + 16*x1^5 - 6*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2, 2*x1^2 - 2*x1 + 1, 4*x1^2 - 5*x1 + 2, 3*x1^2 - 3*x1 + 1, 5*x1^3 - 8*x1^2 + 5*x1 - 1, 2*x1^3 - 6*x1^2 + 4*x1 - 1, 3*x1^2 - 4*x1 + 2]