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