File:TrefoilKnotOrder2Symmetry.png
Jump to navigation
Jump to search
Size of this preview: 441 × 599 pixels. Other resolutions: 177 × 240 pixels | 636 × 864 pixels.
Original file (636 × 864 pixels, file size: 41 KB, MIME type: image/png)
Summary
| Description |
English: The common visualizations of the trefoil knot exhibit its order-3 rotational symmetry (by 120 degrees). But this knot also has two order-2 rotational symmetries (by 180 degrees): (a) about the axis perpendicular to the plane, through the center, and (b) about the Y-axis (i.e., a reflection in the Y-axis followed by flipping all over-under crossings).
The diagram consists of two semicircles (radius 1+√2, centered at (0,1) and (0,-1)) and four 3/8 circles (radius 1, centered at (1,1), (-1,1), (-1,-1), and (1,-1)) that connect smoothly, with three appropriate under-over crossings. |
| Date | |
| Source | Own work |
| Author | Wstomv |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:06, 27 March 2026 | | 636 × 864 (41 KB) | wikimediacommons>Wstomv | Uploaded own work with UploadWizard |
File usage
There are no pages that use this file.
