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 C₂ (Abelian) point group
• A Band with finite width/height and T=1 has one C₂ axis, which can bisect the (idealized) cycle at any arbitrary point
• The C₂ axis intersects at precisely two points on the cycle
• For a band with finite width/height, these points are not equivalent (the C₂ 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