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