  We compare various ways of decomposing and decompactifying the string field
theory vertex and analyze the relations between them. We formulate axioms for
the octagon and show how it can be glued to reproduce the decompactified
pp-wave SFT vertex which in turn can be glued to recover the exact finite
volume pp-wave Neumann coefficients. The gluing is performed by resumming
multiple wrapping corrections. We observe important nontrivial contributions at
the multiple wrapping level which are crucial for obtaining the exact results.
