An Explanation of the Trinity?

[FallentoReason]

I was trying to work out a plausible explanation of what the Trinity is exactly, metaphysically speaking. The closest I got was to see the Godhead as a sort of "company" where the 3 members of it all have the right to use the company's name, but they are still 3 seperate entities. But then the problem is that God the Father, God the Son and God the Holy Ghost aren't "God" just like Bill Gates isn't "Microsoft". Thus the idea of what we commonly mean by "God" is completely lost. On the other hand, if these 3 employees were God/divine, then since they are 3 separate entities working under the "Godhead", we effectively have polytheism.

Any theists have coherent explanations, or can you fix up my analogy above?

You are looking at the physical...

I explicitly said I was talking about the metaphysical.