# Tagged Questions

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### How many unit balls can be put into a unit cube?

Here a unit ball is a ball of diameter 1, and a unit cube is a cube of edge length 1. A famous counterintuitive fact is that, as the dimension increases, the volume of the unit ball tends to zero ...
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### Electrons on a pancake ellipsoid

The problems of minimizing the potential energy of electrons on a sphere, or maximizing the smallest distance between the electrons, have been well-studied. E.g., see the earlier MO question "...
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### N-balls covering n-balls

This question is a follow-on question from: Covering a unit ball with balls half the radius The questions are these: Given an arbitrary dimension d, and a unit n-ball in d-dimensional Euclidean ...
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### Is the kissing number in $n$ dimensions always divisible by $n$? And what is the base of exponential growth of the kissing number?

And why are the kissing numbers for 1, 2, 3, 4 and 8 dimensions all highly composite numbers?
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### Computing the Volume of Closed 3-Manifolds and the Geometrization Conjecture

My question is whether or not if I generalize Theorem 2(i) of "Contact Graphs of Unit Sphere Packings Revisited" [2012] by K. Bezdek and S. Reid (arXiv link) which states The number of touching ...
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### Which term is better for the so called “sphere packing”?

I'm working on sphere packings. When I write, I'm confused with basic definitions. I'm hesitating between the terms "sphere", "ball" or "oriented sphere". For example, on the wikipedia page of circle ...