Can some body help me with some source code for finding automorphism groups of regular maps?. For example: the type of graph is denoted as $\{p, q\}$, which means that they are tessellations of the plane by regular $p$–gons such that each vertex has coordination number $q$. Essentially I want to find automorphism group of $p=8$ and $q=3 (\{8,3\})$ for large number of vertices, say $n=100000$.
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$\begingroup$ What language are you planning to use, for starters...? $\endgroup$– David Roberts ♦Commented Feb 27 at 5:27
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$\begingroup$ Sorry I could not get you, you mean which programming language? If so then Mathematica, matlab or python. any one. $\endgroup$– Zahid MalikCommented Feb 27 at 6:23
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1$\begingroup$ Or GAP, or MAGMA, or and number of other things, and it wasn't clear that you don't really care about the language. MathOverflow is not a programming service to write the code that you want. Imagine you went to Stack Overflow and just asked people to write your code for you—what would happen, do you think? $\endgroup$– David Roberts ♦Commented Feb 27 at 6:54
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$\begingroup$ Maybe better to ask if there are packages to help with this, in a language of your choice, or resources so you can roll your own in a language that is particularly suited to this type of calculation and so on. $\endgroup$– David Roberts ♦Commented Feb 27 at 6:55
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$\begingroup$ Sorry if you got it in some other way. In my posted question, I have mentioned 'source code' that means I was expecting a starting point to solve my problem. Ofcourse it is not possible to provide an exact code for some problem. $\endgroup$– Zahid MalikCommented Feb 27 at 7:02
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1 Answer
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The "full" automorphism group (that is, the automorphisms of the infinite tiling) will be generated by an elliptic element of order $p$ (rotation about a face centre), an elliptic element of order $q$ (rotation about a vertex), and an elliptic element of order two (rotation about an edge centre). And a reflection, if you allow orientation reversing elements. These are sometimes called triangle groups.
In the euclidean or hyperbolic case, the automorphism group of a patch of the tiling will be finite (at most dihedral, but usually trivial).
