The realization space is
  [1   0   1   0   1    0     1   2*x1 + 1     1    2*x1 + 1           1]
  [0   1   1   0   0    1     1         -1    -1   -2*x1 - 1   -2*x1 - 1]
  [0   0   0   1   1   -1   -x1         x1   -x1          x1          x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-12*x1^6 - 40*x1^5 - 36*x1^4 - 8*x1^3)
avoiding the zero loci of the polynomials
RingElem[2, x1, 2*x1 + 1, x1 + 1, x1 + 2, x1^2 + x1 + 1, x1 - 1, x1^2 - x1 - 1, 3*x1 + 2]