From: "R.W.Dirksen" Newsgroups: sci.math Subject: Re: topology: ring of tetrahedrons Date: Tue, 25 Mar 1997 12:17:04 +0100 Brian Hutchings wrote: > > In a previous article, scholten@wolfenet.com (Scholtens) says: > > I think, it'll work with any set of regular (identical) tetrahedra, > more than 6; they are just hinged at the edges, > each tetrah.having a pair of opposite edges joined > to other tetrah. I think, > you can find it in one of Martin Gardener's books. > > >that there is a "ring of tetrahedrons" which will fold inside out or > >something. Does someone know of an Internet source for a pattern to use to > >make one of these (I'm not interested in cutting out tetrahedrons > > -- > > first, the bad news. > > http://inet.uni-c.dk/~sch-inst/radio.html This ring of tetrahedrons can be made by 1 pattern of 24 triangles: |\ /|\ /|\ /| | \ / | \ / | \ / | | /|\ | /|\ | /|\ | |/ | \|/ | \|/ | \| |\ | /|\ | /|\ | /| | \|/ | \|/ | \|/ | | /|\ | /|\ | /|\ | |/ | \|/ | \|/ | \| \ | / \ | / \ | / \|/ \|/ \|/ In this pattern all angles are 60° Then you must fold all | one way and all \ and / the other way. Then you almost have it. Stick the sides together to obtain a string of tetraeders and then connect beginning and end to get your "caleidocycle". This one can turn his inside out. Try the same procedure for 8 columns of 4 triangles Good luck!