how many 3D figures that do not have triangular faces are there

Here is some information on platonic solids

http://www.mathsisfun.com/platonic_solids.html

and here is a bit mor detail if you want it.

http://davidf.faricy.net/polyhedra/platonic_solids.html

Heaps 

An infinite number maybe. 

To name a few

Cube

Sphere

Bananas

Lollipops

If you are referring to the five Platonic solids then there are only two of them, the cube and the dodecahedron, that do not have triangular faces.