It's technically a circle rather than a sphere (the highlighting does make it look sort of three-dimensional), but the most famous company I know of that has a logo that could be described in that way is AT&T. If it's on something old, their 1984 "Death Star" logo fits the description even better.
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Sphere
A ball (sphere) has an infinite number lines of symmetry.
it really dependa on the deets
If by parallel, you mean two lines that do not intersect, yes, it is possible to draw them on the surface of a sphere. They will end up being circles, and most pairs will not be equal in size. If you add the idea that the two lines also continue to infinity to the definition, then you cannot draw such things on the surface of a sphere.
forighn money sign