The realization space is
  [1   1   0          1   0   1        2*x1   1      0   2      2]
  [0   1   1   2*x1 - 1   0   0           0   1   2*x1   1   2*x1]
  [0   0   0          0   1   1   -2*x1 + 1   1      1   1      1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-64*x1^5 + 288*x1^4 - 304*x1^3 + 120*x1^2 - 16*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, 3*x1 - 1, x1 - 1, 2*x1^2 - 4*x1 + 1, 4*x1 - 1, 2, 2*x1 + 1, 3, 4*x1 - 3]