The realization space is
  [1   0   1     1   0   1     1    0   1     1]
  [0   1   1   -x1   0   0     0    1   1   -x1]
  [0   0   0     0   1   1   -x1   -1   1    x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^6 - 4*x1^5 - 4*x1^4 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2, x1 - 1, x1 + 1, x1 + 3, x1 + 2]