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.

Square manifolds

These are the best known manifolds. There are eight of them shown as follows:

Square Uncapped cylinder Möbius strip Torus Klein figure 8 Klein bottle Real projective plane Sphere
http://teamikaria.com/dl/zebnuw8TVYvi5oa7PHJFVXjeWIzl6j5b_OqpV9YRZnQ1HR5q.png http://teamikaria.com/dl/HGJdxDSgKdFFmJwMx3NmaeeTiQYuIdQTfVqyhFLWxV8c60WH.png http://teamikaria.com/dl/iCJxkx0R_t4XE_yO1bF8QpBRH-XMi5nDn-ELIknrjyQDa9X8.png http://teamikaria.com/dl/K0bGhfOG3hetb1QT2ev6gCwfdT_JioJJVxSOe65WDn2pyrQW.png http://teamikaria.com/dl/LpJNtb-p34CMW2XuXAEHxPWu_Yo2bx-gXbyxr8eOQU8xdJAr.png http://teamikaria.com/dl/GonihCjgciwA83T8wiya7qsB93p4mpXIi2_t-EWe11UwKv71.png http://teamikaria.com/dl/4h4Ag96nOfc3GRzA8r_rwcqoGURpR8NFiLFWJ9VogyAGV2az.png 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.

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