The realization space is
  [1   1   0   0                  2                  2   0                 2                 2                  2                  2]
  [1   0   1   1   -x1^2 + 6*x1 - 4   -x1^2 + 6*x1 - 6   0                 2                 0   -x1^2 + 6*x1 - 4   -x1^2 + 6*x1 - 6]
  [1   0   1   0                  2                  0   1   x1^2 - 4*x1 + 4   x1^2 - 4*x1 + 4               2*x1               2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - 6*x1 + 4, x1^4 - 10*x1^3 + 34*x1^2 - 48*x1 + 20, x1^2 - 6*x1 + 6, x1 - 2, x1^3 - 6*x1^2 + 6*x1 - 2, x1 - 4, x1^2 - 4*x1 + 2, x1^4 - 10*x1^3 + 34*x1^2 - 44*x1 + 24, 2, x1^3 - 7*x1^2 + 10*x1 - 6, x1^2 - 4*x1 + 6, x1^2 - 5*x1 + 2, x1^3 - 6*x1^2 + 8*x1 - 2, x1^4 - 10*x1^3 + 34*x1^2 - 44*x1 + 20, x1^4 - 10*x1^3 + 32*x1^2 - 40*x1 + 20]