The realization space is
  [1   0   1                  x1   0   1    0   2*x1^2 - 2*x1 + 1                  x1                x1^2                x1^2]
  [0   1   1   2*x1^2 - 2*x1 + 1   0   0    1   2*x1^2 - 2*x1 + 1   2*x1^2 - 2*x1 + 1   2*x1^2 - 2*x1 + 1   2*x1^2 - 2*x1 + 1]
  [0   0   0                   0   1   1   -1         2*x1^2 - x1                x1^2                x1^2         2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-12*x1^12 + 66*x1^11 - 162*x1^10 + 230*x1^9 - 206*x1^8 + 120*x1^7 - 45*x1^6 + 10*x1^5 - x1^4)
avoiding the zero loci of the polynomials
RingElem[2*x1^2 - 2*x1 + 1, x1 - 1, 3*x1^2 - 3*x1 + 1, x1, 2*x1 - 1, 4*x1^2 - 3*x1 + 1, 2*x1^3 - 6*x1^2 + 4*x1 - 1, 3*x1^2 - 2*x1 + 1, 2*x1^3 - 5*x1^2 + 3*x1 - 1, 2, 6*x1^3 - 8*x1^2 + 4*x1 - 1]