Genus (InstanceTopic, 3)
From Hi.gher. Space
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| - | The '''genus''' of | + | The '''genus''' of a [[shape]] is equal to how many "holes" it has that fully pierce the shape. |
[[Line (object)|Lines]] always have a genus of zero. If a hole was created it would be split in half. | [[Line (object)|Lines]] always have a genus of zero. If a hole was created it would be split in half. | ||
| - | There are two types of holes that | + | There are two types of holes that a shape can have. ''Pockets'' are holes completely inside the object and cannot be seen by any outside viewer (unless the being viewing the shape is in a higher dimension than the shape itself). Ordinary ''holes'' are ones that can be seen from the outside, for example the hole in a [[torus]]. The only type of hole that can be placed inside a [[polygon]] is a pocket, as creating a normal hole would split the shape in half. |
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| + | It is actually debatable that there may be ''n''-1 possible types of holes in any given ''n''-dimensional shape. | ||
[[Category:Geometrical properties]] | [[Category:Geometrical properties]] | ||
Revision as of 21:57, 15 June 2007
The genus of a shape is equal to how many "holes" it has that fully pierce the shape.
Lines always have a genus of zero. If a hole was created it would be split in half.
There are two types of holes that a shape can have. Pockets are holes completely inside the object and cannot be seen by any outside viewer (unless the being viewing the shape is in a higher dimension than the shape itself). Ordinary holes are ones that can be seen from the outside, for example the hole in a torus. The only type of hole that can be placed inside a polygon is a pocket, as creating a normal hole would split the shape in half.
It is actually debatable that there may be n-1 possible types of holes in any given n-dimensional shape.
