The realization space is
  [1   0   1    1   0   1    0   2*x1 - 1    1         x1   2*x1 - 1]
  [0   1   1   x1   0   0    1   2*x1 - 1   x1   2*x1 - 1        -x1]
  [0   0   0    0   1   1   -1         x1   x1         x1         x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-24*x1^8 + 152*x1^7 - 366*x1^6 + 448*x1^5 - 306*x1^4 + 118*x1^3 - 24*x1^2 + 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 1, x1 - 1, 2, x1^2 + 2*x1 - 1, 5*x1^2 - 4*x1 + 1, x1^2 - 3*x1 + 1, 4*x1 - 1, 2*x1 - 1, 2*x1^2 - 4*x1 + 1]