Manifold (ConceptTopic, 4)
From Hi.gher. Space
(→Cubic manifolds: add) |
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|width="12%" align="center"|[[Möbius strip]] | |width="12%" align="center"|[[Möbius strip]] | ||
|width="12%" align="center"|[[Torus]] | |width="12%" align="center"|[[Torus]] | ||
| - | |width="12%" align="center"|[[Klein | + | |width="12%" align="center"|[[Klein dalma]] |
|width="12%" align="center"|[[Klein bottle]] | |width="12%" align="center"|[[Klein bottle]] | ||
|width="12%" align="center"|[[Real projective plane]] | |width="12%" align="center"|[[Real projective plane]] | ||
Revision as of 02:17, 31 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.
Cubic manifolds
There are 279 unique cubic manifolds out of 611 defined ones. Only sufficient examples and the most interesting are shown in the following table.
Construction is similar to that of the square manifolds: fold up each cubic net and attach the red, blue and green pairs of facets to each other in that order, making sure the triangles line up.
There are 3 more interesting group S3 cubic manifolds. These are SS0, S0S and S1S, and are currently unknown.
