The realization space is
  [1   1   0        1   1   0   2*x1 + 1    0     1    1     1]
  [0   1   1   x1 + 1   0   0          0    1   -x1    1   -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 (-2*x1^6 - 4*x1^5 - 4*x1^4 - 2*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 + 1, x1, x1 - 1, 2*x1^2 - 1, 2*x1 + 1, x1^2 - x1 - 1, x1^2 + 1, 2]