The realization space is
  [1   1   0   2*x1^2 - 2*x1 + 1   0   1   1                   0   2*x1^2 - 2*x1 + 1    1         1]
  [1   0   1          -x1^2 + x1   0   1   0         2*x1^2 - x1          -x1^2 + x1   x1   -x1 + 1]
  [0   0   0                   0   1   1   1   2*x1^2 - 2*x1 + 1                x1^2   x1        x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (32*x1^11 - 168*x1^10 + 380*x1^9 - 486*x1^8 + 387*x1^7 - 198*x1^6 + 64*x1^5 - 12*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2*x1^2 - 2*x1 + 1, 4*x1^3 - 5*x1^2 + 3*x1 - 1, 4*x1^2 - 3*x1 + 1, 4*x1^2 - 5*x1 + 2, 3*x1^2 - 3*x1 + 1, 5*x1^3 - 8*x1^2 + 5*x1 - 1, 8*x1^4 - 13*x1^3 + 11*x1^2 - 5*x1 + 1, 4*x1^4 - 7*x1^3 + 7*x1^2 - 4*x1 + 1]