  Recent discoveries of magnetic long-range orders in the icosahedral
quasicrystal and topological magnetic structures on the icosahedron (IC) as the
hedgehog state and the antihedgehog state have attracted great interest. Here,
we report our theoretical analysis of the dynamical as well as static structure
of the hedgehog-antihedgehog order in the 1/1 approximant crystal (AC). By
constructing the effective magnetic model for the rare-earth based AC, on the
basis of the linear spin-wave theory, the excitation energy is shown to exhibit
the reciprocal dispersion, as a consequence of preservation of the spatial
inversion symmetry by the hedgehog-antihedgehog ordering. The static structure
factor is shown to be expressed generally in the convolution form of the
lattice structure factor and the magnetic structure factor on the IC(s) and the
numerical calculation reveals the extinction rule. The dynamical structure
factor shows that the high intensities appear in the low-energy branch along
the $\Gamma$-X line and the R-$\Gamma$-M line in the reciprocal space.
