Torus-Worlds

[krusader74]

Here's an idea for an exotic sci-fi or fantasy setting: a toroid planet. Quoting from the article's summary:

Torus-worlds are unlikely to exist naturally. But if they did, they would make awesome places for adventure. A large surface area. Regions with very different climate, seasons, gravity and ecosystems. Awesome skies on the interior surface. Dramatic weather. Moons in strange orbits.

The author does a great job detailing what such a world would be like. The same author also muses about a Double Earth--a planet twice as big as earth.

Last year on these forums, there was a post about using a Double Torus as a setting. It's worth noting that a sphere, a torus and double torus each have different geometries:

• A sphere has an Euler characteristic χ=2, meaning it has an elliptic geometry.
• A torus has an Euler characteristic χ=0, meaning it has a Euclidean geometry.
• A double torus has an Euler characteristic χ=-2, meaning it has a hyperbolic geometry.

I'm fascinated by these unusual settings. I also like the idea of a Hollow Earth such as Pellucidar. Has anyone used settings like these in their campaigns?

[Azafuse]

Homer Simpson would rule that world as undisputed Supreme God.
Or he would destroy it dressed like Galactus.

[Red Baron]

There was a cool post on here a while back about how to map on a double torus.

You got this octagon with various edges connecting to each other.

[Red Baron]

found it

[krusader74]

This blog post shows the planar map of a torus, and how to fold and glue edges to recover the torus:



So the torus is not nearly as exciting as the double torus, topologically.

What's interesting about it, as a planet, are things like--

1. Gravitational variations across the surface:

• For an earth-sized fat donut is: 0.3 G gravitation along the equators and 0.65 G along the poles
• For an earth-sized skinny hoop: 1.1 G gravity along the poles but just 0.75 G along the rimward equator. The hubward equator has slightly higher gravity, 0.81 G.

2. A moon can orbit in a few different ways:

• wobble around the outside
• bobbing up and down through the hole
• through the hole in just one direction, making figure eights