What specific shape exemplifies a universe that is flat geometrically but finite topologically?

Answer

Torus (or doughnut shape)

The torus, or doughnut shape, serves as the canonical illustration of a flat topology imposed on a finite volume. In this topological structure, space connects back onto itself in multiple dimensions. For example, if the universe had a toroidal topology, moving off one edge of the observable region in a particular direction would cause an observer to immediately reappear on the opposite edge, analogous to how movement works on a classic arcade game screen. If the universe possessed this characteristic, light rays emitted from a distant galaxy could travel around the universe one or more times before reaching an observer, leading to the potential observation of multiple, spatially separated images of the same distant object in the sky, including potential repeating patterns within the Cosmic Microwave Background.

What specific shape exemplifies a universe that is flat geometrically but finite topologically?

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The Bizarre Shape Of The Universe - YouTube

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