The realization space is
  [1   0   1           1   0   1    0          x1           1          x1          x1]
  [0   1   1   -2*x1 + 1   0   0    1          x1   -2*x1 + 1   -2*x1 + 1   -2*x1 + 1]
  [0   0   0           0   1   1   -1   -2*x1 + 1          x1          x1    2*x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^4 + 8*x1^3 - 12*x1^2 + 6*x1 - 1)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1 - 1, 3*x1 - 1, x1, 5*x1^2 - 4*x1 + 1, 2, 4*x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, x1^2 + 2*x1 - 1, 6*x1^2 - 4*x1 + 1]