Date: Thu, 23 Feb 95 10:25:57 CST
From: rusin (Dave Rusin)
To: hopd@aol.com
Subject: Re: Polyhedra model making

In article <3ihd3n$56m@newsbf02.news.aol.com> you write:
>I've been interested in polyhedra for some time and have made many models
>with cardboard and Elmer's glue. This method is slow and messy and the
>models are fragile. Also, once the polygons are glued together they're not
>reusable.

This method works well: make the faces out of cardboard but along each edge
leave a small tab running the length of the edge but folded back. When you
want to join two faces along an edge, the tabs should stick out roughly 
perpendicular to the faces, the tabs of the two faces touching 
surface-to-surface. Then run a rubber band around this protruding pair of
tabs to hold them surface-to-surface. This will keep the polyhedron's
faces adjoined at the edges.

>I've designed two kinds of triangular panels, the first kind fitting
>together at the edges to make a tetrahedron, the second kind fitting
>together at the edges to form  an octahedron.

Of course the attempt to provide solid, attachable polyhedral faces
will imply only a finite set of types of triangles (up to congruence,
that is); this rather limits the constructions possible. I don't see a
way around this commercially unless you stretch rubber surfaces over
adustable edges somehow.

>Those interested in a more detailed description and drawings of my panels
>can leave their mailing address at HopD@aol.com or send it to Box 39, Ajo,
>Arizona 85321. There's no charge for the description.

Please send.

>I am hoping that there are polyhedra enthusiasts out there who will help
>me.

Count me in as an enthusiast. Latest discovery: it is possible to construct
a polyhedron with the following properties:
(1) All edges are triangles
(2) Every pair of vertices is joined by an edge
(3) Topologically, the polyhedron is a torus (the surface of a donut).

dave