The realization space is
  [1   1   0   0   1   1        0                  x1^2 - x1      x1 - 1              x1                       x1^2]
  [1   0   1   0   1   0       x1                       x1^3        x1^2            x1^2                       x1^3]
  [0   0   0   1   1   1   x1 - 1   x1^3 - 2*x1^2 + 2*x1 - 1   x1^2 - x1   x1^2 - x1 + 1   x1^3 - 2*x1^2 + 2*x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^10 - 15*x1^9 + 51*x1^8 - 102*x1^7 + 133*x1^6 - 119*x1^5 + 74*x1^4 - 31*x1^3 + 8*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^2 - x1 + 1, x1, x1^3 - 3*x1^2 + 2*x1 - 1, 2*x1^2 - 2*x1 + 1, x1^4 - 3*x1^3 + 5*x1^2 - 3*x1 + 1, 2*x1^2 - x1 + 1, 2*x1 - 1]