Möbius Band as Simplicial Complex

Here we join up the top and bottom surfaces, but with a half twist.

So we get a one sided surface with a single external boundary line.

In the program FriCAS (described here) there is a function: moebiusBand which generates a minimal triangulation of a Möbius band.

(2) -> moebiusBand()

        +1  2  3+
        |2  3  4|
   (2)  |3  4  5|
        |1  4  5|
        +1  2  5+
  Type: FiniteSimplicialComplex(VertexSetAbstract)

More detail, for instance, mapping Möbius band to circle on page here.

EuclideanSpace

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Where Are You

This is one of a series of pages about topology, these pages start here.

For other pages, on the site, about topology see:

• Open Sets
• Fibre bundles
• Simplectical Complexes
• Delta Complexes
• Homotopy
• Homology

Computer Code Implementation

I have written some code to implement algebraic topology structures. This is described on the page here and the actual code is on GitHub here.

Geometry

Here we are concerned with the topology of the möbius band. For a discussion of the geometry see page here. If you need to paramertise it see page here.