Here are some ways of modeling various Shapes:
Homotopy Type | As Cell Complex | |
---|---|---|
Circle | ![]() |
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n-sphere | ![]() |
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Torus | ![]() |
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Möbius Band | ![]() |
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Projective Space | ![]() |
|
kleinBottle |
For more information about constructing shapes as cell complexes see the page here.
N-Sphere
Here is more detail about constructing the n-sphere using paths.
0-sphere | 1-sphere | 2-sphere | 3-sphere |
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and so on... |
The 0-sphere consists of 2 points. There is no non-trivial structure for higher dimensions. | The circle (1-sphere) consists of:
There is no non-trivial structure for 3D and above. |
The hollow sphere (2-sphere) consists of:
There is no non-trivial structure for 3D and above. |
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Could the circle be constructed using just one base point and one line? | ![]() |
Contractibility of Singletons
see page here.