Cellularization for exceptional spherical space forms and the flag manifold of [formula omitted].

We construct an explicit equivariant cellular decomposition of the (4 n − 1) -sphere with respect to binary polyhedral groups, and describe the associated cellular chain complex. As a corollary of the binary octahedral case, we deduce an S 3 -equivariant decomposition of the flag manifold of SL 3 (R). [ABSTRACT FROM AUTHOR]