The realization space is
  [1   0   1   x1^2 - 2*x1 + 1   0   1    0    1   x1^2 - 2*x1 + 1      x1 - 1]
  [0   1   1         -2*x1 + 1   0   0    1    1         -2*x1 + 1    2*x1 - 1]
  [0   0   0                 0   1   1   -1   x1        -x1^2 + x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^7 + 14*x1^6 - 20*x1^5 + 15*x1^4 - 6*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1^2 + x1 - 1, x1 - 1, x1 + 1, x1^2 - x1 + 1]