The realization space is
  [1   1   0   0          1      1   0   2*x1 - 1   2*x1 - 1          1      1]
  [0   1   1   1   2*x1 - 1   2*x1   0          0   2*x1 - 1   2*x1 - 1   2*x1]
  [0   1   1   0          0      1   1         x1         x1         x1     x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (12*x1^6 - 28*x1^5 + 24*x1^4 - 10*x1^3 + 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, 2, 2*x1 - 1, 2*x1^2 - 2*x1 + 1, 4*x1^2 - 6*x1 + 3, 4*x1^2 - 2*x1 + 1, 4*x1^2 - 5*x1 + 2, 4*x1^2 - 3*x1 + 1]