The realization space is
  [1   1   x1^2 - x1 + 1   0   0   1   -x1^2 + 2*x1 - 1   x1^3 - 2*x1^2 + 2*x1 - 1    0   x1 - 1    1]
  [1   0              x1   1   0   1                  0                  x1^2 - x1   x1       -1   x1]
  [0   0               0   0   1   1                 x1             -x1^2 + x1 - 1    1       -1    1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^12 + 12*x1^11 - 35*x1^10 + 63*x1^9 - 76*x1^8 + 63*x1^7 - 35*x1^6 + 12*x1^5 - 2*x1^4)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1, x1^2 - x1 + 1, 2*x1^2 - 2*x1 + 1, 2*x1 - 1, x1^4 - 2*x1^3 + 4*x1^2 - 3*x1 + 1, x1^3 - 2*x1^2 + 3*x1 - 1]