From:rusin@vesuvius.math.niu.edu (Dave Rusin)Date:15 May 1997 17:35:32 GMTNewsgroups:sci.mathSubject:Re: Torus shaped polyhedra???

In article <5le682$c1m@mp.cs.niu.edu>, David Rusin <rusin@cs.niu.edu> 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 dave