Genus (InstanceTopic, 3)
From Hi.gher. Space
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In 3D, the '''genus''' of a [[shape]] is equal to how many "holes" it has that fully pierce the shape. For example, a [[sphere]] has genus 0, and a [[torus]] has genus 1. | In 3D, the '''genus''' of a [[shape]] is equal to how many "holes" it has that fully pierce the shape. For example, a [[sphere]] has genus 0, and a [[torus]] has genus 1. | ||
Latest revision as of 22:57, 11 February 2014
In 3D, the genus of a shape is equal to how many "holes" it has that fully pierce the shape. For example, a sphere has genus 0, and a torus has genus 1.
In higher dimensions, it gets more complicated: with each new dimension, a new type of hole is possible. So each of the different four-dimensional torii have a pair of numbers as their "genus".
This is closely related to homology groups.
