There are some shapes, in architecture and design, which are very difficult to represent with NURBS (mathematical representation). Have a look to the picture n1. You can see something like a fork with two branches. When you see this shape in rendered mode it seems perfect, but when you switch from rendered mode to shaded mode you will see the complexity of the geometry.
It is composed by quadrilateral surfaces and trimmed surfaces. So, a shape so simply could be very difficult to control for some characteristics of continuity between surfaces which make the whole shape. In the other hand we can work with mesh by changing the topology of the polyhedral surface. So only one surface with the right number and position of vertices, edges and faces. In this post I tried to work with mesh in Rhinoceros (not good to work with this representation), adding interesting plug-in like Evolute Tools Lite (Free) and Weaver Bird (free) which increase the power of the main software (Rhino)...without adding cost of license.
I start from a cube with six faces and eight vertices; in Rhino is almost impossible to work with mesh, but luckily there are free plug-in that allow to manage an open or close polyhedral surface: for example the lite version of Evolutetools and Weaver Bird to add at the usual tools of Rhino for meshes. following the sequence of images (n3) you can understand how to create a fork shape. You can add tessellated box to create branches and with a boolean union you will get only one mesh. But remember that box is a poly-mesh so you must weld vertices that are in the same position. Here we go, we have got a perfect core mesh, it is ready to be subdivided by catmull clark algorithm, which is a tool of Weaver Bird. In this way we can reach the desired shape with just one surface (mesh) and the correct topology.
This procedure is useful for product design. Below a video where I show how to use a core mesh in Rhino. While I modify the core mesh, in another window I can see the subdivided surface and check the final shape.