A friend of mine says that in back in school (a long time ago! ) he was told the name for a 3 dimensional figure with 64 sides. He seems to remember it sounds something like
rhomi-cossi-doedcahedron
Does anyone know the correct name and where I might be able to find a picture? I’ve spent a while searching but couldn’t find anything.
Here’s a page of names. A 64 sided polyhedron would be called a hexacontakaitetragon.
Oops, just noticed that is the name of a 64 sided polygon. By extension, I would say a 64 sided polyhedron would be hexacontakaitetrahedron.
I’d say there might be several names, since we can’t be talking about a REGULAR polyhedron with 64 sides. Without stopping to think about it, I would guess that there may be multiple polyhedra with 64 sides and some property making them interesting enough to have been named.
You may have been remembering the name right, and the count of sides wrong:
The rhombicosidodecahedron has 62 faces:
http://www.scienceu.com/geometry/facts/solids/rh_icosidodeca.html
Thanks Cabbage and yabob. 
This message board is great. The answer to any question at all - in less than 1 hour!
[geek mode]Unless of course, you count the bastard children of the semi-regular polyhedra, the prisms and antiprisms.
What I’m talking about: take two regular 62-sided polygons. Put one over the over, and link their edges with squares. That’s the 64-sided prism. If you rotate one of the 62-gons so that each vertice centers on a face of the other, and link with triangles, that’s the 64-sided antiprism. [/geek mode]
[geek mode]
I count 126 faces on your antiprism. Each side of the base has one triangle and each vertex has one triangle. That would be 62+62+2 = 126 faces.
Please check your geek mode calibration.
[/geek mode]
And I thought this was going to be some uber-geek D&D related thread!
BTW, your prism isn’t a regular polyhedron, which was my point. “regular” means a polyhedron all of whose faces are composed of identical regular polygons. If you insist that the polyhedron is also convex (a property people usually implicitly assumed in discussions like this), there are only five of them possible, also called “platonic solids” - the cube, the octahedron, the tetrahedron, the icosohedron and the dodecahedron. My original point was that any polyhedra with 64 faces will neccesarily have more then one type of face, and probably require a name reflecting its more complex nature.
Or a name non-descriptive of its composition, like “prism” or “soccer ball”.
I think the OP was actually thinking of the 62-sided rhombicosidodecahedron since he had the name right except for the spelling. That one is one of the 13 possible “archimedean solids” or semi-regular convex polyhedra, so it sometimes comes up as an important sort of geometrical figure.
It can have the same type of face, it’s just that the face can’t be a regular polygon. An easy way to picture an example of a polyhedron with a given even number of faces is to picture a pyramid with half that many sides (not counting the base), these can all be congruent triangles; now take another pyramid just like it and put the bases together.
Correct, Cabbage. Thank you. I didn’t speak precisely enough.
Quoth yabob:
Not quite-- For a Platonic solid, you also have to add the condition that the same number of faces meet at each vertex. Otherwise, you can stick two tetrahedra or two equilateral pentagonal-based pyramids together, and add two extra figures.
Also correct, Chronos. If I had thought about the usual way you prove it, I would have realized I left something out. OK, what ELSE did I goof up?
The word you’re looking for is pseudorhombicuboctahedron.
I’ve known it for ages, the early 80s at least, from a popular science magazine (I think it was called Science Digest). I looked it up using Google and found a couple of links, but all the mathematical links were out of date.
Thank you, MrWhy. You’ve just validated my existence with this one. 