  In the literature, it is known that near the Takhtajan-Babujain point of the
bilinear-biquadratic spin-$1$ chain, the low energy theory is captured by three
Majorana fermions with a mass sign change, or three Ising chains near the
transition. In this paper, we study how the spin-$1$, the Ising spins, and the
fermions are related at lattice scale. We construct the spin-$1$ operator out
from the Ising spins and fermions, showing that when the Ising chains are in
the ordered phase, the spin-$1$ chain is in the dimer phase, and when the Ising
chains are in the paramagnetic phase, the spin-$1$ chain is in the Haldane
phase. Through this mapping we can see how unit cell doubling in the dimer
phase and the boundary spin-$\frac12$ zero mode in the Haldane phase take
place, even though in the Ising transition neither phenomena exist.
