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