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