Section a polyhedra Section b flag Construction Section C

Geometry on the Internet.

Having surfed thousands of websites pertaining to Geometry I have chosen these as sites that I feel could be of interest to anyone who enjoys Geometry and would like to explore the subject further. I have a particular interest in Polyhedra and that is where my emphasis lies. Some of the sites in this section are in BOLD TYPE and these I feel are particularly worth a visit. I have also put others in LARGER BOLD TYPE and these are the sites that I found more interesting and I have spent much more time on them. There are some sites in this Section that deal with other aspects of Mathematics and I thought that they would be worth including.

These Flag Construction sites are from the Flags of the World website and show how precise the construction of National Flags is. The most complex one is the flag of Nepal and this is an excellent test of a student’s ability to follow instructions and use the necessary geometry equipment.

By the way the whole of the Flags of the World website is full of the History and the Geography of the countries of the world. It is well worth spending some time on this site.

Section C Origamic Architecture

The Origamic Architecture( Pop-ups) are a good way of exploring 3 dimensions and, in Japan, they are used by Architectural students at University level. Books by Prof Chatani give excellent value for money.

The Paper Models are both cheap, (many are free downloads) and are great fun for the students to do. The variety of models on the web that are available is amazing.

This is just a small selection of books that are available and that I use in my own studies on Polyhedra.

I gather that this year (2006) is the Web’s 15^th year in operation and it is truly amazing to see what is on there and the rate at which it is growing. I have only scratched the surface of available Geometry sites and will continue to look for more sites that are of use to anyone that has an interest in the subject.
Section A

My Number 1 site is emphasized as, in my opinion, it is the best site and has literally millions of Polyhedra and their nets all downloadable. The software is very user friendly and Robert Webb regularly upgrades the software. There is a limited free trial download to try. The software is certainly a lot cheaper than the books that I have on the subject of Polyhedra. Anyhow this short list of 9 websites would make a good starting point for viewing and, hopefully, will whet your appetite to look through the numbered list that follows.

By being on line and clicking on one of the websites in this document you should be able to access the site without having to type in the address. If this fails to work then just copy and paste the site in the address bar of your server window. But in general one click will take you to the site.
I hope you can find something that is of interest and that you can use in your teaching programme.

http://web.aanet.com.au/robertw/Stella.html

http://www.georgehart.com/virtual-polyhedra/vp.html

http://mathworld.wolfram.com

http://www.coolmath4kids.com/polyhedra.html

http://www.physics.orst.edu/~bulatov/polyhedra/index.html

http://www.ics.uci.edu/~eppstein/junkyard/

http://www.korthalsaltes.com/

http://www.steelpillow.com/polyhedra/

http://britton.disted.camosun.bc.ca/jbpolyhedra.htm

Number 1 Great Stella

This is THE NUMBER ONE SITE for Polyhedra Software.

I have, over the years, spent a small fortune on books on Polyhedra and in comparison this software is Cheap. If you are serious about Polyhedra … Buy.
Number 2 Non Orthogonal Polyhedra

http://arxiv.org/pdf/cs.CG/0110059

An interesting but rather technical PDF.

This site has 19 Polyhedra. They can be printed as GIFs or PSs. By using PS and opening in Coreldraw you are able to colour individual polygons and to change the size of the resulting models. There is also reference to a Windows programme called Flatland.

The Waterman polyhedra are the result of packing spheres and this site illustrates this very well.

Great graphics.
Number 5 Polyhedra

http://bca.cryst.bbk.ac.uk/bca/cnews/books/Sep97.html

This is a book review.

Number 6 Polyhedra Pastimes

http://britton.disted.camosun.bc.ca/jbpolyhedra.htm

This site is a must. There are many interesting things to do and make. There are a lot of useful commercial materials to buy and there are some book reviews. The Investigating Patterns series of books published by Dale Seymour looks a good series and the links on the site are coordinated with the activities and chapters in the second book in the series.

Number 7 Tessellated Polyhedra

http://britton.disted.camosun.bc.ca/jbpolytess.htm

5 neat Polyhedra with Escher type patterns on them. These nets can be printed off.

Number 8 The 4 Regular non-convex polyheda

http://cage.rug.ac.be/~hs/polyhedra/keplerpoinsot.html

An interesting dissertation on the Keplar-Poinsot models with reference to the Golden Section.

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