The realization space is
  [1   1   0   x1^2 - 2*x1 + 1   0   1   1          0   x1^2 - 2*x1 + 1   x1 - 1      x1 - 1]
  [1   0   1                x1   0   1   0   2*x1 - 1                x1      -x1         -x1]
  [0   0   0                 0   1   1   1         x1        -x1^2 + x1      -x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^14 + 15*x1^13 - 49*x1^12 + 95*x1^11 - 117*x1^10 + 90*x1^9 - 41*x1^8 + 10*x1^7 - x1^6)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, 2*x1^2 - 2*x1 + 1, 2*x1^3 - 4*x1^2 + 4*x1 - 1, x1^2 - x1 + 1, x1^2 - 3*x1 + 1, x1 - 1, 3*x1 - 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1, 4*x1^3 - 7*x1^2 + 5*x1 - 1, 2*x1^2 - 4*x1 + 1, x1^3 - 2*x1^2 + 3*x1 - 1]