The realization space is
  [1   0   1            1   0   1        0   x1 - 1    1      x1 - 1]
  [0   1   1   -x1^2 + x1   0   0   x1 - 1   x1 - 1   x1   x1^2 - x1]
  [0   0   0            0   1   1        1       x1    1        x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 5*x1^7 - 13*x1^6 + 22*x1^5 - 24*x1^4 + 16*x1^3 - 6*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - x1 + 1, x1 - 1, 2*x1^2 - 2*x1 + 1]