Depends what it's a sphere OF. A sphere of mass in outer space (i.e., relatively far from other masses) held together by its own gravity can be very stable - it may remain spherical or almost so for millenia. A sphere of water on a table in my kitchen, not so much.
Also depends what kind of stability you're talking about. If you mean, e.g., a hard ball lying on the flat surface -- it's relatively hard to crush (harder than a cube of the same material), but very very easy to roll (unlike a cube of the same material).
How about communication actually being a circle and thus a perfect communication being a perfect circle? More pertinent to the topic I would think.
Then seeing that circle is merely the circumference of a sphere.