As in six equally sized stars all in the same orbit equidistant from each other, like a hexagon? That seems incredibly unlikely. How would that form? Even if the primordial disc of gas and dust somehow coalesces into six even clumps, any outside perturbation (e.g. from forming planets or neighboring star systems) would nudge those clumps out of balance and eventually cause some of them to crash into one another.

For a more likely arrangement, think about our closest neighbor, the Alpha Centauri system. Binary sun-like stars (A & B) dance in a somewhat eccentric orbit, one a bit larger and brighter and the other a bit smaller and dimmer. Then over 10,000 times further out, a faint red dwarf (C, aka Proxima Centauri) circles them both!

Binary stars are very common, supposedly moreso than even lone stars. If you want to imagine a six-member system, starting building it up like Alpha Centauri but with more pairs. Put a very large pair at the center, a midsize pair circling both, then small stars (perhaps independently captured) on the far outskirts. Something like that would at least be a more reasonable starting point.

But your initial thought isn't exactly stupid though; the universe is absurdly huge (far more stars than grains of sand on Earth) so probability is such that even rare or seemingly impossible things are bound to happen somewhere.

It's rather pleasant to consider the way atomic structures and astronomical structures mirror each other.

Unfortunately, no, geocentrism probably still wouldn't hold in that world. There would probably be one main star the others vaguely orbit. In reality probably the stars wouldn't tolerate each other and play nice; they'd subsume one another until there was only one winner.