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Names of polyhedra
By Stephen Tatlow (P1390) on Tuesday, November 23, 1999 - 09:11 am:

What is a fifty sided solid called? ie a six sided solid is a cube

By James Lingard (Jchl2) on Tuesday, November 23, 1999 - 09:55 pm:

Stephen,

As far as I am aware, there isn't a particular name for a fifty-sided solid. The reason for this is probably that there is no fifty-sided regular convex polyhedron (a polyhedron is just a solid whose faces are polygons). A regular polyhedron is basically one whose sides are all regular polygons, all the same size and shape. In fact, the only regular convex polyhedra are:

- tetrahedron (4 sides, all equilateral triangles)
- cube (6 side, squares)
- octahedron (8 sides, all equilateral triangles)
- dodecahedron (12 sides, all regular pentagons)
- icosahedron (20 sides, all equilateral triangles)

It can be proven that these are the only ones, but the only proof that I know is rather long and requires a fair deal of geometry and group theory.

There are other non-convex regular polyhedra, but I don't know what they're all called. In fact it's possible that there's a fifty-sided one of these, in which case it will have a name, but I'm afraid I don't know.

I hope that's of some use - write back if there's anything else you want to know about this, or want explaining further.

James.

By The Editor:

Here is a proof that there are only 5 regular polyhedra, also known as platonic solids. It's actually not as difficult as James makes it sound, and if you know about the angles in regular polygons you should be able to follow it.