Timeline for Is there a midsphere theorem for 4-polytopes?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2012 at 15:05 | comment | added | Hao Chen | @Gil: You are right, P_6*C_3 is the graph of a stacked polytope, but not sphere packable. | |
| May 23, 2011 at 18:02 | comment | added | Gil Kalai | The apollonian case correspond to the class of polytopes known as "stacked polytopes" which are obtained by gluing simplices along facets. Stacked (d+1)-polytopes lead to apollonian sphere packing in d-dimension defined inductively. For dimension > 3 I suspect that the spheres are not necessarily non overlapping but I am not sure. (Maybe we should relac the nonoverlapping requirement...) | |
| May 23, 2011 at 16:21 | comment | added | Igor Rivin | Would that be the circumsphere of the convex hull of the points of tangency? | |
| May 22, 2011 at 17:58 | comment | added | Joseph O'Rourke | @Igor: Thanks!, especially for the Apollonian article, which reminded me of this: For any $d+1$ mutually tangent spheres in $d$ dimensions, There is a unique sphere through their points of tangency, orthogonal to each of the $d+1$ spheres. | |
| May 22, 2011 at 3:02 | history | answered | Igor Rivin | CC BY-SA 3.0 |