Timeline for Classifying/enumerating vertex-transitive simplicial polytopes
Current License: CC BY-SA 4.0
4 events
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| Mar 14, 2021 at 2:30 | comment | added | M. Winter | Another only half-new example is any generic orbit polytope of the orientation preserving symmetries of the tetrahedron (also called the snub tetrahedron, see also here). Combinatorially it is the same as the icosahedron, but it is not regular for most choices of the generating point. And of course, any vertex-transitive (not necessarily regular) polygon counts as well. | |
| Mar 14, 2021 at 0:04 | comment | added | M. Winter | The disphenoidal 30-cell and the disphenoidal 288-cell are further examples. | |
| Mar 13, 2021 at 23:57 | comment | added | M. Winter | A good question. I asked this myself before. I never had the hope for a classification because my feeling was that if I take just any sufficiently wild finite subgroup of $\mathrm O(\Bbb R^d)$ and just any generic point in $\Bbb R^d$ then the convex hull of the orbit of this point under the group has a good chance of being simplicial (as a polytope with generically chosen vertices is simplicial). But of course, this is just a feeling, and sadly, I have no further examples. I have some candidates in mind but I would need to check whether they are actually simplicial. | |
| Mar 13, 2021 at 21:21 | history | asked | Brent Kerby | CC BY-SA 4.0 |