As part of many hobbies (origami, sculpting, construction toys) I often find myself building polyhedra from regular polygons. I am intimately familiar with all of the Archimedean and Platonic solids, and can construct most of the other isohedra, deltahedra, and Johnson solids from memory. The smaller prisms, antiprisms, and trapezohedra are of course trivial. However, I often forget the precise arrangement of faces and vertices for some of the Johnson solids and most of the Catalan solids. Thus, the question that I pose is this:

Where can I find the most complete, robustly indexed, and searchable database of polyhedra?

I would like to use such a database to answer, in short order, questions of the following nature:

Which solid is comprised of exactly eight hexagons and six squares? Which solids are comprised of less than 10 triangles, eight squares, and six hexagons? How many solids can be constructed with exactly 24 edges? What solid with 12 vertices has the most edges (or faces)? etc...

I imagine that such a database does not exist and I am going to be forced to create one, so answers suggesting features for such a database (likely to be web-based) are welcome as well.