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     x1^2 - x1 + 1        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 (x1^12 - 7*x1^11 + 24*x1^10 - 53*x1^9 + 81*x1^8 - 86*x1^7 + 62*x1^6 - 29*x1^5 + 8*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - x1 + 1, x1^2 - 2*x1 + 2, x1^2 + 1, x1^3 - x1 + 1, 2*x1 - 1]