The realization space is
  [1   1   x1 - 1   0   0   1    1   x1 - 1                  0      x1^2 - 2*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   x1^3 - 2*x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-3*x1^10 + 23*x1^9 - 79*x1^8 + 160*x1^7 - 211*x1^6 + 188*x1^5 - 113*x1^4 + 44*x1^3 - 10*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - x1 + 1, 3*x1^2 - 3*x1 + 1, 2*x1 - 1, 2*x1^2 - 2*x1 + 1]