Problem with 3D game data storage

I am making a 3D game with OpenGL (via LWJGL) and I have been using a 3 dimensional array to store every vertex from models. (for collision detection, and knowing what is where)

From the World class:

Code Java:

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		this.length = 700;
		this.width = 700;
		this.height = 700;
		this.multiplier = 100;
		this.data = new GameObject[length][height][width];

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But when I do this, I run out of heap space. This seems like an obviously bad way of doing things, but I don't know how else to do it.

I had 2 possible ideas:

1. There is another, better way of storing large amounts of data

2. I make a method like this

Code Java:

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public List<GameObject> allObjectsInWorld = new ArrayList<GameObject>();
 
public GameObject getObjectAt(int x, int y, int z)
{
       for(int i = 0; i < allObjectsInWorld.size(); i++)
       {
             GameObject cur = allObjectsInWorld.get(i);
 
             for(int j = 0; j < cur.model.vertices.length; j++)
             {
                   if(cur.model.vertices.get(j) == new Vector3f(x, y, z))
                   {
                           return cur;
                   }
             }
       }
       return null;
}

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