The realization space is
  [1   0   1    1   1   0    3   1    1   0    1]
  [0   1   1   -1   0   0    0   1    2   2   -1]
  [0   0   0    0   1   1   -1   1   -1   1   -1]
in the integer ring
within the vanishing set of the ideal
240ZZ
avoiding the zero loci of the polynomials
RingElem[2, 3, 5]