  We propose an exotic multi-qubit Toffoli gate protocol via asymmetric Rydberg
blockade, benefiting from the use of a spheroidal configuration to optimize the
gate performance. The merit of a spheroidal structure lies in a well
preservation of strong blocked energies between all control-target atom pairs
within the sphere, which can persistently keep the blockade error at a low
level. On the basis of optimization for three different types of
$(2+1)$-$qubit$ gate units to minimize the antiblockade error, the gate
fidelity of an optimal $(6+1)$-$qubit$ configuration can attain as high as
$0.9841$ mainly contributed by the decay error. And the extension with much
more control atoms is also discussed. Our findings may shed light on scalable
neutral-atom quantum computation in special high-dimensional arrays.
