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