Manifold (ConceptTopic, 4)
From Hi.gher. Space
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== Cubic manifolds == | == Cubic manifolds == | ||
| - | There are | + | There are 279 unique cubic manifolds out of 611 defined ones. Only sufficient examples and the most interesting are shown in the following table. |
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!style="background-color: #EEE;"|Group 2 | !style="background-color: #EEE;"|Group 2 | ||
!style="background-color: #EEE;" colspan="2"|Group 3 | !style="background-color: #EEE;" colspan="2"|Group 3 | ||
| - | !style="background-color: #EEE;" colspan=" | + | !style="background-color: #EEE;" colspan="3"|Group S |
|- | |- | ||
|align="center"|1 defined | |align="center"|1 defined | ||
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|align="center"|64 defined | |align="center"|64 defined | ||
|align="center" colspan="2"|512 defined | |align="center" colspan="2"|512 defined | ||
| - | |align="center" colspan=" | + | |align="center" colspan="3"|26 defined |
|- | |- | ||
|align="center"|1 unique | |align="center"|1 unique | ||
| Line 64: | Line 64: | ||
|align="center"|36 unique | |align="center"|36 unique | ||
|align="center" colspan="2"|216 unique | |align="center" colspan="2"|216 unique | ||
| - | |align="center" colspan=" | + | |align="center" colspan="3"|20 unique |
|- | |- | ||
|align="center"|1 shown | |align="center"|1 shown | ||
| Line 70: | Line 70: | ||
|align="center"|2 shown | |align="center"|2 shown | ||
|align="center" colspan="2"|3 shown | |align="center" colspan="2"|3 shown | ||
| - | |align="center" colspan=" | + | |align="center" colspan="3"|5 shown |
|- | |- | ||
| - | |align="center" width=" | + | |align="center" width="12%"|[[Cube]] |
| - | |align="center" width=" | + | |align="center" width="12%"|[[Dihose]] |
| - | |align="center" width=" | + | |align="center" width="12%"|[[Toric hose]] |
| - | |align="center" width=" | + | |align="center" width="12%"|[[Ditorus]] |
| - | |align="center" width=" | + | |align="center" width="12%"|[[Toric bottle]] |
| - | |align="center" width=" | + | |align="center" width="12%"|[[Toraspherinder]] |
| - | |align="center" width=" | + | |align="center" width="12%"|[[Toraspherindric bottle]] |
| + | |align="center" width="12%"|[[Toraspherindric dalma]] | ||
|- | |- | ||
|align="center"| | |align="center"| | ||
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|align="center"|[[Real projective realm]] | |align="center"|[[Real projective realm]] | ||
|align="center"| | |align="center"| | ||
| - | |align="center"|[[ | + | |align="center"| |
| - | |align="center"|[[ | + | |align="center"|[[Spherical hose]] |
| + | |align="center"|[[Glome]] | ||
|} | |} | ||
[[Category:Topology]] | [[Category:Topology]] | ||
Revision as of 01:55, 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.
| Group 0 | Group 1 | Group 2 | Group 3 | Group S | |||
|---|---|---|---|---|---|---|---|
| 1 defined | 8 defined | 64 defined | 512 defined | 26 defined | |||
| 1 unique | 6 unique | 36 unique | 216 unique | 20 unique | |||
| 1 shown | 2 shown | 2 shown | 3 shown | 5 shown | |||
| Cube | Dihose | Toric hose | Ditorus | Toric bottle | Toraspherinder | Toraspherindric bottle | Toraspherindric dalma |
| Möbial hose | Real projective planar hose | Real projective realm | Spherical hose | Glome | |||
