Genus (InstanceTopic, 3)
From Hi.gher. Space
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There are two{{hmm}} 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. | There are two{{hmm}} 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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Revision as of 22:28, 16 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.
