All of the models included in my collection (or models created by others equivalent to them).

Platonic solids 
Kepler–Poinsot polyhedra 
Archimedean solids 
Catalan solids 
Uniform star polyhedra 
Dual uniform star polyhedra 
Prisms 
Bipyramids (dual uniform) 
Bipyramids (regular faces) 
Antiprisms 
Trapezohedra 
Cupolas and cuploids 
Trapezopyramids and keratinoids