property within an interface of same name C#

Solution 1:

Here is what came to my mind first. Not sure if this answers your question though but let's say you are implementing a Linked list data structure. You will probably have some kind of a Node to represent the values in the list:

class LinkedList<INode>
{
    public INode Head { get; set; }
}

interface INode
{
    INode Next { get; set; }
}

class Node : INode
{
    public object Value { get; set; }
    public INode Next { get; set; }
}

The interface implementation can be used to ensure that the class will have a reference to itself in order to represent the next element in the linked list.

Solution 2:

There are plenty of use-cases where a type may have a property of itself. Imagine a Person. Every instance of that class may have Children, which themeselves Persons as well and may have other Children.

class Person
{
    public Person Child;
}

In your case one may argue that a box may live within another box or may contain other boxes.

Or let´s think of a Box as a surrounding rectangle around some geometric figure. Of course that bounding-box is a geometry in itself, so it may have a bounding-box also (which however will be pretty much the same).