Timeline for Which polytopes can be folded to an edge?
Current License: CC BY-SA 4.0
7 events
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| Aug 16, 2023 at 15:32 | comment | added | Pritam Majumder | @IlyaBogdanov Ah! I see, Thanks. I think that works. So basically, we start with a node $v$, then fold the edges incident to $v$ to a single edge $vv_1$, then fold the rest of the edges incident to $v_1$ to an edge $v_1v_2$, and so on. And this works for any bipartite graph with equal edge lengths (need not be skeleton graph of a polytope) | |
| Aug 16, 2023 at 9:21 | comment | added | Ilya Bogdanov | Is it possible to implement a physical argument? Let the skeleton (where vertices are hinges) hand on one fixed vertex $u$. The bipartite structure allows all verticves to fit into a single line (each vertex's distanve to $u$ is just the graph distance), and this clearly priviides the minimum of the pitential energy. The only question is --- if you really hang the skeleton, would it indeed move to that state? (Surely, it iseasy to pass from this state to a one-edge.) | |
| Aug 16, 2023 at 9:17 | comment | added | Ilya Bogdanov | If you colour the vertices in black and white, each edge has vertices of differ4nt colours. So, fixing one edge, all others should be put there in a unique manner. | |
| Aug 16, 2023 at 9:09 | comment | added | Pritam Majumder | @IlyaBogdanov Yes continuous folding (the usual physical folding, i.e. the edges can not cross during folding). Could you please elaborate why it is obvious? | |
| Aug 16, 2023 at 8:26 | comment | added | Ilya Bogdanov | Are you asking about continuous folding? The final state for any bipartite skeleton is obvious… | |
| Aug 15, 2023 at 8:38 | history | edited | Pritam Majumder | CC BY-SA 4.0 |
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| Aug 15, 2023 at 8:04 | history | asked | Pritam Majumder | CC BY-SA 4.0 |