wendy wrote:In four dimensions, one can pack at least 24, and prehaps 25 spheres around a sphere.
anderscolingustafson wrote:So the maximum number of spheres you can pack around a sphere in 4d might just be the same as the number of sides to the 120 cell.
Tamfang wrote:anderscolingustafson wrote:So the maximum number of spheres you can pack around a sphere in 4d might just be the same as the number of sides to the 120 cell.
Might be, but isn't. You need to restrain this impulse to apply analogies blindly.
anderscolingustafson wrote:I wander how many spheres could be packed around a sphere in five dimensions.
wendy wrote:That's why the kissing pennies trick doesn't work.
The case in 4d is for the coins around the sphere to be 0.61803398875 = 0:74.19 of the central size.
... There are not a lot of polytopes of high symmetry that equate to packing small spheres around a big one.
In any case, the three-dimensional case uses larger spheres than the pennies (the edges of 3,5 are bigger than the radius). The kissing sphere of some size is the right approach, ...
wendy wrote:The idea of the geodesic dome is to use a minimum number of strut sizes to get a maximum dome. That's the point.
The 'kissing pennies' trick supposes that the coin in the middle is the same size as the external ones.
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