Timeline for Iterated polyhedron face twisting
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 19, 2019 at 18:36 | comment | added | Joseph O'Rourke | @JeppeStigNielsen: It would be especially interesting if there were fixed points in a non-trivial sense---reached after more than just 1 iteration. | |
| Jul 19, 2019 at 16:54 | comment | added | Jeppe Stig Nielsen | You could use another $\theta$, like $\theta=\pi=180^\circ$. This time other polyhedra are "fixed points" in the most trivial way. You could also go back to the plane polygon where you rotate edges around their midpoints, and pick an "arbitrary" but fixed $\theta$. | |
| Jul 19, 2019 at 16:27 | comment | added | Joseph O'Rourke | @JeppeStigNielsen: Nice observations--Thanks! | |
| Jul 19, 2019 at 16:26 | comment | added | Jeppe Stig Nielsen | In addition there is the infinite sequence hexagonal antiprism, enneagonal antiprism, dodecagonal antiprism, etc.; they are also non-deltahedra for which $P_1$ equals $P_0$ in the most trivial way. | |
| Jul 19, 2019 at 15:35 | comment | added | Jeppe Stig Nielsen | Trivially, the faces can also be regular $3k$-gons and still stay fixed under that rotation, so e.g. the truncated tetrahedron (having only regular hexagons and equilateral triangles as faces) is also a "fixed point". | |
| Jul 19, 2019 at 14:56 | history | asked | Joseph O'Rourke | CC BY-SA 4.0 |