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