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!