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