Why are there two lines going through the top of my project?
That’s where you divided the surface to make the Dots. Don’t know how to fix, but you now know what the problem is.
Check you mesh for extra geometry (vertices), try W-Remove Doubles.
And, please, do use a proper Topic Title.
don’t know if that’s the technique you used, but I think the best is to add your plane (face of the cube) and then your 3 circles (at the same level that the plane). you must delete the face of the plane (X key => only faces). then you join the 3 mesh together (crtl+j in object mode), then select all vertices (A key), and eventually shit+F to make the faces.
then to make the hollow part, you can either extrude and resize the circles in order to make em look like a sphere, or use 3 spheres from the begining, instead of the circles. (but when making the faces, select only the mid vertices.
hope this will help