The realization space is
  [1   0   1   0   1    0   x1    2           2*x1        x1         2]
  [0   1   1   0   0    1   x1   x1   -x1^2 + 4*x1   -x1 + 4   -x1 + 4]
  [0   0   0   1   1   -1    4    4              8      2*x1      2*x1]
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 + 2, x1 - 2, x1 - 4, x1 + 4, 2, x1 + 8, x1 - 1, x1, x1^2 - 8, x1^2 - 4*x1 - 8]