How to make 3D object from random points using three.js?

Question

I generate 10 random points. I want connect each point to every another and get faces for every flat area. So, it will nice 3D object with invisible flat faces inside.

How is it possible to make faces from geometry of 10 random points?

var objects3 = [];
var geometrySpline = new THREE.Geometry();
  for ( var i = 0; i < 10; i ++ ) {                 
      x = Math.floor(Math.random() * (max - min + 1)) + min;
      y = Math.floor(Math.random() * (max - min + 1)) + min;
      z = Math.floor(Math.random() * (max - min + 1)) + min;
      n = new THREE.Vector3( x, y, z );
      objects3.push( n );
   }
   for ( var x = 0; x < (objects3.length); x ++ ) {
       for ( var x2 = 0; x2 < (objects3.length); x2 ++ ) {
            geometrySpline.vertices.push(objects3[ x ]);
            geometrySpline.vertices.push(objects3[ x2 ]);
       }        
   }

Answer 1

THREE.ConvexGeometry  appears to work as   WestLangley suggested

Here's a jsfiddle

http://jsfiddle.net/cwoodall22/bk3qx8ys/