Möbius strip variation (Gulchenko's eight)

The illustrated figure is a topological object with the characteristics of a Möbius strip (a Möbius loop). The figure is a one-sided surface.

It appears that the object has two closed contours. But actually those contours consist of one single closed two-dimensional contour. The following correlation can be observed in the case of this figure: two seemingly closed three-dimensional objects effectively consist of one two-dimensional surface.

Creation of the object:

1) Take a square sheet of paper (with the corners A, B, C and D) Extend each of the four corners with rectangular strips.
2) The opposite corner strips of the sheet must be connected to each other (A with C; B with D)
3) With the A-C pair one of the two corner strips is given a half twist in a clockwise direction before being connected. With the B-D pair one of the two corner strips is given a half twist in a counter-clockwise direction before being connected.
4) After the clockwise half twist, the A and C corner strips are glued together from the front side of the square. After the counter-clockwise half twist, the other two corner strips (B and D) are glued together from the reverse side.

If a movement on the objects surface is projected onto a horizontal surface, it is found that this results in a closed movement on the X and Y axes, unlike the situation with a classic Möbius strip where the movement projection is restricted by one axis.

The figure is symmetrical when viewed from all six main vantage points even though the components appear to be asymmetrical.

Category:

Science & Technology

Tags:

• Möbius
• strip
• Mobius
• topology
• surface
• geometry
• one-sided

[Ruthlesscritic]

The interesting thing is that, as found by tracing, it has 2 edges or boundries, but still one surface, whereas a classic mobius strip has only one edge in addition to only having one surface.

[redmtal]

very cool