The realization space is
  [1   1    1   1   1    1    1    1    1   0    0   0   0]
  [1   1    1   0   0    0   -1   -1   -1   1    1   0   1]
  [1   0   -1   1   0   -1    1    0   -1   0   -1   1   1]
in the integer ring
avoiding the zero loci of the polynomials
RingElem[2, 3]