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