Manifold (ConceptTopic, 4)
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A '''manifold''' is a [[shape]] formed from a [[regular]] base shape, where various edges are connected either with or without twists. | A '''manifold''' is a [[shape]] formed from a [[regular]] base shape, where various edges are connected either with or without twists. | ||
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== [[Square]] manifolds == | == [[Square]] manifolds == | ||
- | These are the best known manifolds. | + | These are the best known manifolds. There are eight of them shown as follows: |
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- | + | {| | |
- | + | |width="12%" align="center"|[[Square]] | |
+ | |width="12%" align="center"|Uncapped [[cylinder]] | ||
+ | |width="12%" align="center"|[[Möbius strip]] | ||
+ | |width="12%" align="center"|[[Torus]] | ||
+ | |width="12%" align="center"|[[Klein figure 8]] | ||
+ | |width="12%" align="center"|[[Klein bottle]] | ||
+ | |width="12%" align="center"|[[Real projective plane]] | ||
+ | |width="12%" align="center"|[[Sphere]] | ||
+ | |- | ||
+ | |align="center"|http://teamikaria.com/dl/zebnuw8TVYvi5oa7PHJFVXjeWIzl6j5b_OqpV9YRZnQ1HR5q.png | ||
+ | |align="center"|http://teamikaria.com/dl/HGJdxDSgKdFFmJwMx3NmaeeTiQYuIdQTfVqyhFLWxV8c60WH.png | ||
+ | |align="center"|http://teamikaria.com/dl/iCJxkx0R_t4XE_yO1bF8QpBRH-XMi5nDn-ELIknrjyQDa9X8.png | ||
+ | |align="center"|http://teamikaria.com/dl/K0bGhfOG3hetb1QT2ev6gCwfdT_JioJJVxSOe65WDn2pyrQW.png | ||
+ | |align="center"|http://teamikaria.com/dl/LpJNtb-p34CMW2XuXAEHxPWu_Yo2bx-gXbyxr8eOQU8xdJAr.png | ||
+ | |align="center"|http://teamikaria.com/dl/GonihCjgciwA83T8wiya7qsB93p4mpXIi2_t-EWe11UwKv71.png | ||
+ | |align="center"|http://teamikaria.com/dl/4h4Ag96nOfc3GRzA8r_rwcqoGURpR8NFiLFWJ9VogyAGV2az.png | ||
+ | |align="center"|http://teamikaria.com/dl/6DfUWpRUCTvIcPzgXCfjaVzgQueSMNorAmgm8o87JArm5GhR.png | ||
+ | |} | ||
- | + | To construct, first connect the red edges to each other, matching up the arrowheads, and then connect the blue arrows together in the same way. Edges without arrows are left unconnected. | |
- | + | The Klein figure 8 and Klein bottle are topologically equivalent, however they have been listed separately as they appear significantly different. | |
[[Category:Topology]] | [[Category:Topology]] |
Revision as of 22:24, 30 August 2008
A manifold is a shape formed from a regular base shape, where various edges are connected either with or without twists.
Square manifolds
These are the best known manifolds. There are eight of them shown as follows:
To construct, first connect the red edges to each other, matching up the arrowheads, and then connect the blue arrows together in the same way. Edges without arrows are left unconnected.
The Klein figure 8 and Klein bottle are topologically equivalent, however they have been listed separately as they appear significantly different.