Best Shape for TIR: Glass Container | Optics Discussion

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For a container made of glass, what geometrical shape of the container would be best for maximum Total Internal Reflection, given that light incident on it is coming after reflection from a concave mirror?

My hunch is that a cylindrical shape of the container is best, but I was not so sure after the shape of a Diamond came into my mind! (I'm not very good in Optics! :D). What do you guys think is the best shape?
 

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Your set-up isn't clear to me. Does the 'container' have to contain anything? Where is the container to be in relation to the real image formed by the concave mirror?
 
The set-up is simple. Light rays from everywhere possible, hit a concave reflecting surface, and the container is placed in close proximity to it (strategic placement of the container would be so as to have maximum amount of light entering it), so that light rays entering it undergo maximum TIR. Yes, the container is to have "something" in it potentially that would make illumination of the light best, but I think it would make the set-up complicated. So, for now, just assume it's hollow.

For simplicity, just assume that a concave mirror is kept on its curved surface on the floor, and the container is placed just above it(not on it!). Now, what should be the shape of the container if whatever light from the reflecting surface is to hit it, and undergo maximum TIR?