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.
Möbius band: One boundary, shown in red: (2) -> moebiusBand() +1 2 3+ |2 3 4| (2) |3 4 5| |1 4 5| +1 2 5+ Type: FiniteSimplicialComplex(VertexSetAbstract) |
This diagram can only be realised in 3D, to make it clearer in 2D I have duplicated nodes 3 and 4: The blue arrows should join up, notice the head of the arrow is at the top on the left and bottom on the right. |
More detail, for instance, mapping Möbius band to circle on page here.