The realization space is
  [1    1   1   0   0   1    1         -x1        0   x1 - 1]
  [1   x1   0   1   0   1   x1           0      -x1      -x1]
  [0    0   0   0   1   1   x1   -2*x1 + 1   x1 - 1   x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^8 + 18*x1^7 - 32*x1^6 + 28*x1^5 - 12*x1^4 + 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, 3*x1^2 - 3*x1 + 1, x1 - 1, x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1]