No, I mean we as in the human race! Sorry if it misled you, I often write that way when the subject is about scientific discoveries - "We have discovered a new planet", "We think the universe is 13.7 billion years old" etc.

This is the original story - Is the universe a dodecahedron?

And the paper that followed the original story -
A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map

A research group then pursued the issue but they found no evidence for any non-trivial topology across a diameter of 78 billion light years (24 Gigaparsecs) and so we can confidently state that the fundamental domain of the whole universe is at least that large. These figures are based on the WMAP data representing a sphere around us that has now grown to 46 billion light years in radius (92 billion light years diameter). They intend to continue the search until they have reached ~28 Gigaparsecs. They have discounted the dodecahedral model as the universe would have had to have had a fundamental domain only 30 billion light years across for that to work.

This is the paper with their findings - Extending the WMAP Bound on the Size of the Universe.

I actually agree with you about the universe probably being a hypersphere but if the fundamental domain of the universe is indeed larger than our observable portion of it, as seems likely, we will never know for sure. If the fundamental domain were smaller however (and that is a possibility), we might find evidence that allows us to determine the overall topology. (See I'm doing the we thing again - I just fall into it naturally!)

Until they have finished the study, I wouldn't want to commit myself either way, even if I thought the most plausible shape was an S3 hypersphere. The reason is simple - if they find no evidence for a non-trivial topology at all then the whole universe must be larger than our observable portion of it. The topology will therefore always be subject to speculation.