The shape of the universe is a matter of debate in physical cosmology over the local and global geometry of the universe which considers both curvature and topology, though, strictly speaking, it goes beyond both. In practice, more formally, the debate seeks a 3-manifold that corresponds to the spatial section (in comoving coordinates) of the 4-dimensional space-time of the universe.
The recent Wilkinson Microwave Anisotropy Probe (WMAP) measurements have led NASA to state, "We now know that the universe is flat with only a 0.5% margin of error." Within the Friedmann–Lemaître–Robertson–Walker (FLRW) model, the presently most popular shape of the Universe found to fit observational data according to cosmologists is the infinite flat model, while other FLRW models that fit the data include the Poincaré dodecahedral space and the Picard horn.
Read more about Shape Of The Universe: Introduction, Local Geometry (spatial Curvature), Global Geometry
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“The structure was designed by an old sea captain who believed that the world would end in a flood. He built a home in the traditional shape of the Ark, inverted, with the roof forming the hull of the proposed vessel. The builder expected that the deluge would cause the house to topple and then reverse itself, floating away on its roof until it should land on some new Ararat.”
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—Ursula K. Le Guin (b. 1929)