## Summary of the Properties of a Möbius band with
T=1π

- Only a Band with finite width/height is disymmetric
(chiral). It belongs to the C
_{2} (Abelian) point group
- A Band with finite width/height and T=1 has one
C
_{2} axis, which can bisect the (idealized) cycle at any arbitrary point
- The C
_{2} axis intersects at precisely two points
on the cycle
- For a band with finite width/height, these points
are
**not** equivalent (the C_{2} Abelian point group
has no degeneracies)
- A journey starting at any arbitrary point on the surface
takes
**two** traversals of the cycle to return to the
starting point.
- In the limit, a cycle with zero width/height
**lies
exclusively in 2D space**

© H. S. Rzepa