One power of octrees is that they are able to provide a representation of just about any arbitrarily shaped object; whether it is convex, concave or has interior holes. The precision is determined only by the size of the smallest cell. This is a major consideration for applications such as raytracing, where the accuracy of objects is crucial in achieving good results.
Secondly, such properties as surface area, volume, centre of mass, and interference are easily calculated at different levels.
Operations on octrees are another advantage, because they display the same ease and efficiency of use as quadtrees due to the simplicity of the tree structure.