Timeline for What is the symmetry group of this compound of two polytopes?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Feb 5, 2021 at 2:36 | comment | added | Will Sawin | Shouldn't the edge length be $2 \sqrt{6}$ here? (Or $\sqrt{6}$ if you normalize the hypercube edge length to $1$.) | |
| Feb 3, 2021 at 13:55 | comment | added | Richard Stanley | In fact, a regular simplex of dimension $n$ can be inscribed in a hypercube of dimension $n$ if and only if $n+1$ is the order of a Hadamard matrix. If we also want every automorphism of the simplex to extend to an automorphism of the hypercube, then the $n=2^m-1$ result is correct. | |
| Feb 3, 2021 at 11:22 | answer | added | Adam P. Goucher | timeline score: 7 | |
| Feb 3, 2021 at 8:24 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title, made title more explicit
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| Feb 3, 2021 at 3:55 | history | edited | Daniel Sebald | CC BY-SA 4.0 |
Fixed error
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| Feb 3, 2021 at 3:55 | comment | added | Daniel Sebald | Later on in 4.5: “The proof of the ‘only if’ part of the statement of the last theorem may have seemed a bit unclear to the reader, and that is because it is false.” | |
| Feb 3, 2021 at 3:11 | comment | added | Tom Goodwillie | You can't even have a triangle of vertices with side lengths $\sqrt 3$. | |
| Feb 3, 2021 at 2:53 | comment | added | Gerry Myerson | "Theorem 4.5. A regular simplex of dimension n can be inscribed in a hypercube of dimension n if and only if $n=2^m −1$ for some m." $n=11$ is not of that form. | |
| Feb 3, 2021 at 2:53 | comment | added | Daniel Sebald | Oops, you’re right. | |
| Feb 3, 2021 at 2:52 | history | edited | Daniel Sebald | CC BY-SA 4.0 |
edited body
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| Feb 3, 2021 at 2:39 | comment | added | Gerry Myerson | Wouldn't that hypercube have edges of length $2$, not $1$? | |
| Feb 3, 2021 at 2:19 | comment | added | Daniel Sebald | Are you sure about that? | |
| Feb 3, 2021 at 2:08 | history | edited | Daniel Sebald | CC BY-SA 4.0 |
added 504 characters in body
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| Feb 3, 2021 at 1:27 | comment | added | Tom Goodwillie | There is no such simplex. | |
| Feb 3, 2021 at 0:47 | history | asked | Daniel Sebald | CC BY-SA 4.0 |