What Are the Kissing Numbers for Different Sized Spheres in 3D?

Click For Summary
Kissing numbers refer to the maximum number of spheres that can touch another sphere of the same size in three-dimensional space, with the standard number being 12 for equal-sized spheres. When considering smaller outer spheres, the kissing numbers become more complex and do not align neatly with platonic solids, leading to potentially irregular results. The discussion indicates that while the kissing number for equal-sized spheres is well-established, variations with different sizes may not have readily available solutions. The complexity arises from the geometric arrangements of the smaller spheres. Further research is needed to determine the kissing numbers for spheres of varying sizes.
jal
Messages
544
Reaction score
0
I am looking for info on kissing numbers.
If all the spheres are of one unit then there are 12 spheres in 3d that can kiss the center sphere.
Question:
If the outer spheres are smaller by say 1/4, 1/2 etc. what would be the kissing numbers?
I assume that this has already been done but my search has not found anything.
jal
 
Physics news on Phys.org
The reason it works out nice for spheres of equal size is because the dodecahedron has 12 faces. I think the answer is going to be ugly for sphere kissings that don't correspond to platonic solids.
 

Similar threads

Undergrad Higher Dimensional Spheres viz. Cubes
  • · Replies 1 ·
Replies
1
Views
1K
3D object inverted w.r.t. a sphere
  • · Replies 1 ·
Replies
1
Views
4K
High School What Is the Fourth Dimension and How Does It Work?
  • · Replies 3 ·
Replies
3
Views
2K
What is the mapping between the hyperriemann sphere and the complex plane?
  • · Replies 4 ·
Replies
4
Views
2K
Four Dimensional Bowling Alley & Billiard Hall
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What is the name of the software company behind the MSG Sphere in Las Vegas?
  • · Replies 1 ·
Replies
1
Views
2K
What does having 3d symmetry 2d symmetry and 1d symmetry mean?
  • · Replies 36 ·
2
Replies
36
Views
2K
High School Calc Excess Rad on Earth in Curved 3D Space | Feynman Lectures 6-2
  • · Replies 29 ·
Replies
29
Views
3K
Formula derivation connecting vertical water flowrate & horizontal distance moved by a suspended sphere
  • · Replies 207 ·
7
Replies
207
Views
9K
Doublet flow in Fluid Dynamics between two spheres or cylinders
  • · Replies 0 ·
Replies
0
Views
2K