  We study the alternating $k$-arm incipient infinite cluster (IIC) of site
percolation on the triangular lattice $\mathbb{T}$. Using Camia and Newman's
result that the scaling limit of critical site percolation on $\mathbb{T}$ is
CLE$_6$, we prove the existence of the scaling limit of the $k$-arm IIC for
$k=1,2,4$. Conditioned on the event that there are open and closed arms
connecting the origin to $\partial \mathbb{D}_R$, we show that the winding
number variance of the arms is $(3/2+o(1))\log R$ as $R\rightarrow \infty$,
which confirms a prediction of Wieland and Wilson (2003). Our proof uses
two-sided radial SLE$_6$ and coupling argument. Using this result we get an
explicit form for the CLT of the winding numbers, and get analogous result for
the 2-arm IIC, thus improving our earlier result.
