Timeline for Are there any other regular compounds?
Current License: CC BY-SA 4.0
11 events
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| S Jan 23, 2021 at 18:54 | history | suggested | gmvh |
Added top-level tag (every question should have an arXiv-style top-level tag)
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| Jan 23, 2021 at 17:53 | review | Suggested edits | |||
| S Jan 23, 2021 at 18:54 | |||||
| S Jan 23, 2021 at 16:20 | history | edited | Daniel Sebald |
edited tags
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| Jan 23, 2021 at 11:41 | review | Suggested edits | |||
| S Jan 23, 2021 at 16:20 | |||||
| S Jan 23, 2021 at 10:50 | history | edited | M. Winter |
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| Jan 23, 2021 at 10:41 | comment | added | M. Winter | To find such compounds you would need to take a symmetry group of a regular polytope, and embed it as subgroup of a larger point group. I suspect that your list is complete. Though I wonder whether there is an easy way to see that $\mathrm{Aut}(A_n)$ cannot be enlarged in dimensions $n\ge 9$. For sufficiently large dimensions, the answers to this question suggests that $B_n$ can never be enlarged because it is the largest point group there is. | |
| Jan 23, 2021 at 7:43 | review | Suggested edits | |||
| S Jan 23, 2021 at 10:50 | |||||
| Jan 23, 2021 at 3:41 | comment | added | Daniel Sebald | Most of those are not flag-transitive, though. Wikipedia seems to prefer Coxeter’s definition. | |
| Jan 23, 2021 at 2:19 | comment | added | Sam Hopkins | I had never even heard the term "compound of polytopes" before your post but Wikipedia seems to have a list here: en.wikipedia.org/wiki/…. I also note the quote "Coxeter lists 32 regular compounds of regular 4-polytopes in his book Regular Polytopes. McMullen adds six in his paper New Regular Compounds of 4-Polytopes." which might be especially relevant to your question. | |
| Jan 23, 2021 at 1:18 | review | First posts | |||
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| Jan 23, 2021 at 1:11 | history | asked | Daniel Sebald | CC BY-SA 4.0 |