The realization space is
  [1   0   1   0   1   0          1         x1         x1          1]
  [0   1   1   1   1   0   x1^2 + 1   x1^2 + 1   x1^2 + 1   x1^2 + 1]
  [0   0   0   1   1   1       x1^2         x1       x1^2         x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^12 + 6*x1^11 - 17*x1^10 + 31*x1^9 - 41*x1^8 + 41*x1^7 - 31*x1^6 + 17*x1^5 - 6*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 + 1, x1 - 1, x1^2 - x1 + 1, x1 + 1]