Exercise for the Modeling Fundamentals tutorial flow by Jonathan Williamson. The sphere and cone were relatively easy using a combination of loop cuts, bevels, insets and the knife tool. The corners in the sphere were relatively hard. Not sure what the easiest method would be.
I opted to bevel the boundary edges of the cube twice to create two thin strips. After selecting these strips, I deselected the center parts of the strips that should not be cut. I then proceeded to perform the cuts using the inset tool.