The realization space is
  [1   1   x1 - 1   0   0   1    1   x1 - 1                  0      x1 - 1]
  [1   0       x1   1   0   1    0       x1                 x1        x1^2]
  [0   0        0   0   1   1   x1   x1 - 1   -x1^2 + 2*x1 - 1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^10 + 8*x1^9 - 28*x1^8 + 58*x1^7 - 81*x1^6 + 81*x1^5 - 58*x1^4 + 28*x1^3 - 8*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1^3 - x1^2 + 2*x1 - 1, x1 - 1, x1, x1^2 - x1 + 1, x1^2 + 1, 2*x1 - 1]