  A Casimir--type analysis of the effect of dividing the two--sphere by several
lines of latitude is done for conformally invariant Dirichlet and Neumann
scalars and for spinors. An effective action combination is shown to have
minima for symmetrical arrangements of the circles. For a domain of two caps
and a slice, the Dirichlet slice expands to fill the whole sphere while the
Neumann one adjusts to an angular separation of 57.92 degrees. The fermion
expression is written in terms of the Weber class function, $\gf$, and a
connection is noted with an earlier calculation of twisted scalar effective
actions on the tetrahedron.
