How do I make all vertices in a mesh equidistant from one another?

They all doesn't have to be perfectly equidistant but just as long as it's equidistant enough.
I know that I need to iterate over every vertex in the mesh for every vertex in the mesh using a nested for loop, and than check if the distance from the vertex from the outer loop and the inner loop have a distance less than some threshold. But after that part how can I actually move the vertices so they are "equidistant"?

 

Do you have an example? It's kind of hard to grasp what you're trying to do, there's only one 3D shape with vertices all equidistant from each other and that's a triangular pyramid.

 

Here are images of what trying to equidistantify
https://www.reddit.com/r/Unity3D/co...from/?utm_medium=android_app&utm_source=share