What is the physical, geometric shape of the universe?
Ok, maybe you have some misconceptions.

The Universe has no center at all. It looks the same from avaery point, to wherever you look to. It is approximatedly as follows:



This image represents a very large scale box on our universe on current time (not on perceived time, based on received light). Of course, it is just a computer simulation. Each dot represents a cluster of galaxies.

So you need to imagine an infinite tridimensional space filled with filament-like structures like these. And infinite means it has no bounds, so it has no "external" shape. No ball, rugby-ball nor cone there. Also not irregular external shape, just infinite. Any of these shapes have a 2D boundary on a 3D space, but the universe has no boundary.