Frequently Asked Questions about the Atlas of Small Regular Polytopes

Actually, I've never been asked any of these. However, I imagine they might become frequently asked in the distant future, if I did not put the answers here.

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• What is the Atlas?
• It's a collection of web pages providing information about a number of small regular abstract polytopes. It includes information about all regular abstract polytopes whose automorphism groups have order less than or equal to 2000, except 1024 and 1536.

• Will you include polytopes of order 512, 1024 and 1536 soon?
• Order 512 are in! They were added in February 2007. The other cases are not practical with the current level of theory and computing technology.

• What is the "Atlas Canonical Name"?
• The Atlas Canonical Name is a unique identifier given to each polytope in the Atlas. It won't change, so it can be used in publications. It has three parts. The first part is the Schlafli symbol of the polytope. This is followed by an asterisk, then the order of the polytope's automorphism group. If there is more than one polytope with given Schlafli type and group order, the polytopes are distinguished by affixing a, b, c, etc to their names.

• What does "SmallGroup(x,y)" mean?
• GAP provides enumerations of all groups of order up to 2000, except for orders 1024 and 1536, thanks to Eick et al. These groups may be accessed by the SmallGroup command in GAP. SmallGroup(x,y) returns an element of the yth isomorphism class of groups of order x.

• Can I get my own copy of the Atlas?
• Yes. This 13Mb file contains a program written in GAP that will generate the web pages of the Atlas. Given the right combination of CPU time, RAM, OS and plain old good luck, your computer will churn out the over 500Mb of html files that are available at this site. I did it on a Linux machine, using the command gap.sh -o 256m < mkatlas.gap

• Why didn't you include information about property X on your polytope pages?
• Most likely, I didn't think of it. If there is information you feel should be included, feel free to email me (my email address may be found below). If you can provide GAP code that can calculate the information from the special generators of the automorphism group of the polytope, that would be ideal. Next best would be a clear algorithm, unless the algorithm is already known to me. If the information is hard to capture algorithmically, well, email me anyway.

• How do I cite the Atlas in a publication?
• Currently, the best citation to use is :
  M. I. Hartley, "An Atlas of Small Regular Polytopes", To Appear: Periodica Mathematica Hungarica (2006).
  Check back here for updates.

• Are there other lists of abstract regular polytopes available online?
• Yes. You may be interested in polytopes whose automorphism groups are almost simple groups of order up to 1000000 or sporadic simple groups up to the Held group.

• My question is not answered here!
• Send me an email! My email addresses are mike40033 at gmail dot com, and Michael dot Hartley at nottingham dot edu dot my.