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Question: All distances of point to point on the sphere are to be integer.

Question:All distances of point to point on the sphere are to be integer.

Tokoro 115 Maple
integer sphere
March 03 2022
1

The two points on the sphere has radius r=1/2. So, the distance is 1.
The three points on the sphere has radius r=1/sqrt(3). So, all distances are 1.
The four points on the sphere has radius r=sqrt(6)/4. So, all distances are 1.
What is the smallest sphere radius for 5 points and above numbers?  

Find the smallest sphere radius and 3D position of each point.

Answer of smaller radius is better.

Tokoro.


 

All distances of point to point on the sphere to be integer.
The two points on the sphere has radius r=1/2. So, the distance is 1.
The three points on the sphere has radius r=1/sqrt(3). So, all distances are 1.

The four points on the sphere has radius r=sqrt(6)/4. So, all distances are 1.
What is the smallest sphere radius for 5 points and above numbers?  Find the smallest sphere radius and 3D position of each point.

> 

with(plots)with(GraphTheory); with(LinearAlgebra); with(SpecialGraphs)
> 

with(plottools)

NULL

The answer of 4 points. r=sqrt(6)/4

   

plots[display]([c, nodes, plotlinesx], scaling = constrained, style = wireframe, axes = boxed)

  

NULL


 

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