In cylindrical polar coordinates, the cylinder is a surface of constant radial coordinate r, while a wedge is the surface of constant angular coordinate θ.
Interaction between a tilted wedge and a plate:
"Casimir force between sharp–shaped conductors,"
M.F. Maghrebi, S.J. Rahi, N. Graham, T. Emig, R.L. Jaffe, & M. Kardar, preprint (2010)
Highly accurate analytical expressions can be obtained by a multiple-reflection series.
E.g., for the knife edge,
Other interesting limits:
Dark side of the moon: