Manifold (ConceptTopic, 4)

From Hi.gher. Space

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Revision as of 22:28, 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:

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
I	+	-	++	+-	-+	--	S

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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 |align="center"|http://teamikaria.com/dl/4h4Ag96nOfc3GRzA8r_rwcqoGURpR8NFiLFWJ9VogyAGV2az.png
 |align="center"|http://teamikaria.com/dl/6DfUWpRUCTvIcPzgXCfjaVzgQueSMNorAmgm8o87JArm5GhR.png
+|-
+|align="center"|I
+|align="center"|+
+|align="center"|-
+|align="center"|++
+|align="center"|+-
+|align="center"|-+
+|align="center"|--
+|align="center"|S
 |}