extruded cut interior on cylindrical face?

Hello everyone,

I'm in the process of modeling some phone cases for the fun of it, and have come across a problem with the four corners of my case. As you can see, the interior walls are extruded to match the phones curved body, but I cannot figure out a good way to create the same feature going around the interior corners. I feel it is easier than it is made out to be, but thought I might post here for some tips and tricks on this problem, as well as for my overall design.

Thanks!

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