From:  (Dave Rusin)
Date:           15 May 1997 17:35:32 GMT
Newsgroups:     sci.math
Subject:        Re: Torus shaped polyhedra???

In article <5le682$>, David Rusin <> wrote...

What rubbish! Who is this guy? Why do they let him post?

>You can fix (?) this by glueing an
>additional block onto each of the  12  faces that's in the middle of a
>coplanar set-of-three.

Nice try, but then the central "hole" is lined with 4 sets of three coplanar
faces. As an alternative, glue an additional block onto each of the 4
faces of each of the four corner blocks.

>As you may already know, if you try to build a polyhedron using only
>regular  n-gons, then the number  m  of them that meet at a vertex is
>limited; indeed the only combinations are  (n,m)=

The listed combinations are the only ones which can occur in _convex_
polyhedra. Of course this does not apply with positive genus.

Those who like this sort of thing will like this book:

    AUTHOR:     Stewart, Bonnie Madison.
    TITLE:      Adventures among the toroids; a study of quasi-convex,        
                   aplanar, tunneled orientable polyhedra of positive genus
                   having regular faces with disjoint interiors ... written,
                   illustrated and hand-lettered by B. M. Stewart.
                                   ^^^^^^^^^^^^^ !
    PUBL.:      (Okemos, Mich., : B. M. Stewart,                              
    FORMAT:     206 p. illus. 34 x 13 cm.
    DATE:       1970