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Basic Information

A Hyperdoughnut is a higher dimensional space that is shaped like a doughnut. Since the geometric name of the shape of a doughnut is Torus, a hyperdoughnut is also known as a hypertorus. As with a doughnut, from any point on the surface of a hyperdoughnut you can trace two circles that converge back on the spot. One goes the long way around the outer circumference of the doughnut, the other goes the short distance towards (and back from) the empty space of the doughnut hole.

One major difference between a 3-D doughnut and a hyperdoughnut is that light curves around the hyperdoughnut. So, your plane of existence were a hyperdoughnut, if you looked far enough ahead in one direction (or 180 degrees reversed from that direction), you'd see the back of your head, just as if you were on a Hypersphere. However, unlike a hypersphere, this image of you would not persist in every direction. Instead, if you turned your head 90 degrees to the right of that line, you'd again see yourself, but this time in profile. You'd see the left side of your body, and the back of your head turned away. If you then turned your head to look towards the other shoulder you'd again see yourself, but now you'd see the right side of your body, and again the back of your head.

Of the two axis for such observations, one will end up being longer than the other, because one traces the entire circumference of the doughnut and the other traces just one section of it. This means in two directions your apparent other selves will be closer to you, and the two apparent other selves in the other two directions will appear further away. Of course, if the hyperdoughnut is really large, you might not be able to see either version of yourself without a telescope.

See Also:
Fourth Dimension


1. Book: Hyperspace by Michio Kaku
2. Wikipedia on Torus - includes an illustration of how you can divide the surface of a torus into seven sections for mapping purposes.

Game and Story Use

  • Could make for interesting Topology if an Extradimensional Space, City In A Bottle or Pocket Universe were shaped as a Hyperdoughnut.
    • It also wouldn't be quite as bad a mapping nightmare as a Hypersphere is, at least not once you understood the shape of reality. There's ways to visualize the doughnut surface as a map projection. Such map projections are also possible with the hypersphere, but on one of those, a single loop takes you past every point of the universe, which would get pretty confusing. On a hyperdoughnut, any given direction only takes you past a subset of landmarks, not every possible point.
      • Though to be honest, I'm not quite sure what would happen if you headed out at an angle that was 45 degrees between the two perpendicular axis. I think you'd twist and corkscrew around the doughnut, and I'm not sure what you'd see ahead of you. I keep meaning to try it out by drawing on an actual doughnut, but then I get hungry and eat them instead. :)
  • Be very careful when firing a ranged weapon on a hyperdoughnut.
    • A laser will shoot you in the back.
    • A bow or gun might or might not be safe, depending on the size of the hyperdoughnut. With some possible doughnut proportions, it might be completely safe in the long direction, but suicidal in the short direction. I fire one way, and the bullet hits the ground before looping around. I turn 90 degrees and fire again, and that bullet hits me in the back.
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