Timeline for The Symmetry of a Soccer Ball
Current License: CC BY-SA 2.5
18 events
| when toggle format | what | by | license | comment | |
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| Jun 23, 2010 at 2:54 | history | edited | mathphysicist |
edited tags
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| Mar 30, 2010 at 20:03 | history | edited | Bill Kronholm | CC BY-SA 2.5 |
restated questions, vagueness removed.
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| Mar 30, 2010 at 19:55 | answer | added | Gordon Williams | timeline score: 1 | |
| Mar 30, 2010 at 19:22 | answer | added | Leah Wrenn Berman | timeline score: 4 | |
| Mar 30, 2010 at 18:42 | answer | added | Spinorbundle | timeline score: 6 | |
| Mar 30, 2010 at 15:13 | comment | added | Bill Kronholm | Thanks for the comments. I was looking for something in the direction of other such objects having non-trivial symmetry groups, although the regularity constraint limited me to a rather small class of objects. I was originally thinking about the duals of these objects, which would be polyhedra built out of regular triangles where either five or six triangles meet at each vertex. These would look like geodesic domes, and I was curious about the symmetry of such geodesic domes. | |
| Mar 30, 2010 at 12:37 | answer | added | Joseph Malkevitch | timeline score: 5 | |
| Mar 29, 2010 at 19:21 | answer | added | Douglas Zare | timeline score: 2 | |
| Mar 29, 2010 at 19:10 | vote | accept | Bill Kronholm | ||
| Mar 29, 2010 at 18:59 | comment | added | Sonia Balagopalan | ias.ac.in/resonance/Jan2001/pdf/Jan2001p28-41.pdf | |
| Mar 29, 2010 at 18:59 | vote | accept | Bill Kronholm | ||
| Mar 29, 2010 at 19:00 | |||||
| Mar 29, 2010 at 18:58 | answer | added | David Eppstein | timeline score: 7 | |
| Mar 29, 2010 at 18:54 | comment | added | Pete L. Clark | Since the question as stated turned out to have a not very interesting answer, would any of the geometers out there like to address what happens when the regularity conditions in 1) are dropped? | |
| Mar 29, 2010 at 18:49 | comment | added | Pete L. Clark | Indeed the soccer ball and the dodecahedron both have rotational symmetry group $A_5$: see en.wikipedia.org/wiki/Icosahedral_symmetry. Are you asking whether any other polyhedron meeting your requirements has symmetry group $A_5$, or nontrivial symmetry group, or what? "Very nice symmetry" is not very precise. | |
| Mar 29, 2010 at 18:45 | answer | added | Anton Petrunin | timeline score: 13 | |
| Mar 29, 2010 at 18:23 | comment | added | Douglas Zare | If you drop the condition of regularity, you can have other combinatorial types. For example, you can join 2 copies of 6 pentagons around a hexagon. See fullerenes for more examples. However, I would guess that these can't be made from regular polygons. I recommend using Polydron models to check. | |
| Mar 29, 2010 at 18:18 | comment | added | Qiaochu Yuan | In case you're curious, the mathematical name for a soccer ball is a truncated icosahedron: en.wikipedia.org/wiki/Truncated_icosahedron | |
| Mar 29, 2010 at 18:08 | history | asked | Bill Kronholm | CC BY-SA 2.5 |