The realization space is
  [1   1   0        x1 - 1   0   1   1         0        x1 - 1         1    1]
  [0   1   1   2*x1^2 - x1   0   0   1        x1   2*x1^2 - x1        x1   x1]
  [0   0   0             0   1   1   1   -x1 + 1     x1^2 - x1   -x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-12*x1^10 + 68*x1^9 - 170*x1^8 + 246*x1^7 - 226*x1^6 + 135*x1^5 - 51*x1^4 + 11*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 2*x1^2 - 2*x1 + 1, 2, 3*x1 - 1, 3*x1^2 - 3*x1 + 1, 3*x1^3 - 5*x1^2 + 4*x1 - 1, x1^2 - x1 + 1, 3*x1^2 - 2*x1 + 1, 3*x1 - 2]