[Webmath] Equal Distances Within a Sphere

[Jonathan Pike]

Hi;
My objective is to discover the exact 3D points for creating Platonic 
solids. Since these are the only geometries that have equal length sides
 and equal angles between them, I thought it might be easiest to find a 
formula that enables me to calculate farthest points within a sphere 
where the lengths and angles are equal. Does such a formula exist?
TIA,
Jonathan
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