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I'm working a file where I need to cut a cross shape into a sphere so that it looks like a guide an artist would use to draw a head, like the following:
However, I'm not sure where to start, I can't seem to manipulate the topology of the sphere in order to do this.
I would use Boolean Modifier. 3 times to be exact.
First cut a sphere shape out of a panel. Do this by moving the panel into the sphere, until the edge of the panel is in the center of the sphere. Then add a Boolean Modifier, select the sphere as the Object and Apply.
(the panel might have missing faces, or an open side. If this happens you'll have to close up the mesh first I'm afraid.)
Then move the panel with the piece cut out of it into a Sphere, only a tiny bit deeper than the previous panel and put a Boolean Modifier on the Sphere this time (and select the panel as the Object), and again apply.
Then rotate the panel 90 degrees and do it again.
(To finish it off you could Shade Smooth the object and putt an Edge Split Modifier on it, to make it look nicer.)
Cut a cross shape as in make the cross slightly indented into the surface? You should already have edges running exactly where you want the cross, so you could try selecting those edges, bevel (ctrl+ b), increase the loops in the middle to two (scroll wheel up two times), then just grab the new faces you’ve made in the middle and pull them in a bit. That should indent a cross shape.
You can select the edges where you want the red line to be, (alt click 2 times, in front and behind), duplicate (shift d), scale it up a bit (s), make a face (f). Then, you can extrude it (e), separate it (p) by selection, add a material and make it red, and sculpt your sphere in material preview mode.
