Sphere packings
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Software
We used Bertini to solve a sphere packing
problem consisting of 12 spheres. We first consider a problem based
on 8 spheres and then use intersection to solve the 12 sphere problem.
8 spheres
We can solve the subproblem of 8 spheres directly
using the regenerative cascade algorithm via
input.
We also solve this by starting with 4 spheres and adding
one sphere at a time using the following files.
- Directly solve for 4 spheres: input
- Extending to 5 spheres: input
- Extending to 6 spheres: input
- Extending to 7 spheres: input
- Extending to 8 spheres: input
12 spheres
We now build from the 8 spheres to solve the 12 sphere problem
using input.
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