This is the title of an excellent book by Magnus Wenninger. Spherical models are projections of polyhedra on a sphere . The book offers very clear explanations of the models and the maths behind them. There is some very valuable mathematics here for able KS4 students, using pythagoras, trigonometry and circle theorems to find angles and sides for the models. They are excellent for visualising the duality of polyhedra. There is also an excellent section on geodesic domes.
Below is a picture gallery of a spherical model of an dodecahedron and it's dual, the icosahedron. The pentagons are the faces of the dodecahedron and the triangles are the faces of the icosahedron. It was a pleasure to make (as you can see from my face in the last picture) and is one of the nicest objects I have ever held. It was constructed from 120 triangular pieces and took around 15 hours. The paper is 150gsm which was easier to cut than 300gsm card (see below), and was stuck together with UHU glue which works well for paper.