Timeline for How are reflection groups related to general point groups?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 29, 2019 at 6:42 | comment | added | Günter Rote | Here is a proof that $G$ is not contained in the symmetry group of a duoprism. We look at great circles that are kept elementwise fixed by nontrivial elements of $G$: A symmetry that rotates a plate $P$ leaves the whole circle $F_i$ on which $P$ lies pointwise fixed. Hence there are 12 great circles that are left fixed by elements of $G$. On the other hand, there are only two choices of a circle that is pointwise fixed by a nontrivial symmetry of a "large enough'' duoprism (the two "axis circles''). | |
| Dec 29, 2019 at 6:29 | history | edited | Günter Rote | CC BY-SA 4.0 |
added notation
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| Dec 28, 2019 at 9:07 | vote | accept | M. Winter | ||
| Dec 28, 2019 at 5:36 | comment | added | Günter Rote | Indeed, 70 can be replaced by any multiple of 10. (10 because the group $I$ (taken as left multiplications) itself already generates 10 points on each circle.) | |
| Dec 26, 2019 at 9:35 | comment | added | M. Winter | Thank you for this elaboration! I think the number 70 plays no particular role here, and we can choose any arbitrarily high number of points on each circle, right? If so, we can make the resulting polytope have more symmetries than any 4-dimensional uniform polytope except for certain duoprisms (14400 might ne the highest number of symmetries, attained for the 120/600-cell). I then believe it might not be too hard to argue that no symmetry group of a duoprism can have the described group as a subgroup. | |
| Dec 26, 2019 at 8:27 | history | edited | Günter Rote | CC BY-SA 4.0 |
added 40 characters in body
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| Dec 26, 2019 at 8:21 | history | answered | Günter Rote | CC BY-SA 4.0 |