The realization space is
  [1   1   0   4*x1^2 - 4*x1 + 1   0   1   1          0   4*x1^2 - 4*x1 + 1   2*x1 - 1      2*x1 - 1]
  [1   0   1                x1^3   0   1   0     x1 - 1                x1^3       x1^2          x1^2]
  [0   0   0                   0   1   1   1   2*x1 - 1       2*x1^3 - 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*x1^10 - 32*x1^9 - x1^8 + 99*x1^7 - 158*x1^6 + 120*x1^5 - 50*x1^4 + 11*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, 2*x1 - 1, 3*x1^2 - 3*x1 + 1, x1^2 + x1 - 1, x1^2 - 3*x1 + 1, x1^3 + 2*x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, 3*x1 - 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1 - 2]