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