A torus is a specific type of toroid, which can be a more general term. Here's a breakdown:
Torus
- A torus is a three-dimensional geometric shape that is often visualized as a ring-like object, similar to a doughnut.
- Mathematically, it's defined as the surface of revolution generated by rotating a circle in 3D space around an axis that lies in the same plane but does not intersect with that circle.
- A torus has a single "hole" through it.
- Examples: A common tire tube, or a doughnut.
Toroid
- A toroid is a more inclusive term. It refers to a surface of revolution with one or more holes.
- According to the reference, a torus is a type of toroid.
- A toroid can be seen as approximating the surface of a torus with a topological genus, g, of 1 or greater.
- The "genus" refers to the number of "holes" or handles. A standard torus has genus 1.
- The shape does not have to be perfectly circular, and can have multiple holes.
- Examples: Toroidal polyhedrons, and shapes similar to a doughnut with one or more additional holes.
- A Toroid is not restricted to a doughnut shape. It can have any number of holes. A torus is a specific example of a toroid, having only one hole.
Table Summarizing the Key Differences
| Feature | Torus | Toroid |
|---|---|---|
| Definition | Specific ring-like shape with one hole | General term for surfaces of revolution with one or more holes |
| Shape | Typically circular with a single central hole | Can have various shapes with one or more holes |
| Holes | One | One or more |
| Relation | A specific instance of a Toroid | A more general category that includes the torus |
In essence, if you see a doughnut, you're looking at a torus, and because it is a ring-like shape, it is also a toroid. However, not all toroids are toruses. A complex shape with multiple holes is a toroid but not a torus.
