A torus (donut shape) that has been extended to higher dimensions.
To help visualize the hypertorus, imagine a spaceship on a 2-dimensional video screen. When the spaceship moves too far to the left, it reappears on the right side of the screen. Thus we can infer that the two sides of the screen are touching. The shape we have now is a cylinder. Now imagine the spaceship going up to the top of the screen and reappearing on the bottom. In order for this to occur, the top of the cylinder must be "folded" so that it touches the bottom of the cylinder. This creates a donut-like torus shape. Here's where it gets tricky. Imagine the spaceships finite but unbounded universe contains a third dimension through which it is able to freely traverse. If it travels a certain distance along its z-axis it again returns to the same place. Because it is as impossible for me to describe what this would look like geometrically as it is for you to imagine, I will simply leave my (admittedly somewhat lacking) description of a hypertorus at that.

If I recall correctly I lifted the video screen analogy from Hyperspace by Michio Kaku. I highly recommend the purchase of this book if you are at all in to upper dimensional geometry or physics.

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