  We investigate several antipodal spherical designs on whether we can choose
half of the points, one from each antipodal pair, such that they are balanced
at the origin. In particular, root systems of type A, D and E, minimal points
of Leech lattice and the unique tight 7-design on $S^{22}$ are studied. We also
study a half of an antipodal spherical design from the viewpoint of association
schemes and spherical designs of harmonic index $T$.
