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Dear Forum,

I have very little experience and

knowledge about groups theory, even though I studied it in 1972.

I read from some books about the 17 wall-paper groups.

I shall mention the following famous ones:

* Hilbert Cohn-Vossen Geometry and Imagination

* Grossman Magnus The groups and their graphs

* Weyl The simmetry

* Coxeter Introduction to geometry

I'm thinking to the very celebrated hollandisch painter M.C. Escher,

mentioned by Coxeter in his previously cited work.

According to Coxeter's notation these groups are represented by these

symbols with the following meaning:

p1 two translations

p2 three half turns

pg two parallel glide reflections

pm two reflections and a translation

cm a reflection and a parallel glide reflection

pmm reflection in the four sides of a rectangle

pmg A reflection and two half-turns

pgg Two perpendicular glide reflections

cmm two perpendicular reflection and a half-turn

pgg two perpendicular reflection and a half-turn

p4 a half turn and a quarter turn

p4m Reflections in three sides of a (45,45,90) triangle

p4g A reflection and a quarter-turn

p3 Two rotations through 120

p3m1 A reflection and a rotation through 120

p31m Reflection in the three sides of an equilateral triangle

p6 A half-turn and a rotation through 120

p6m Reflections in the three sides of a (30,60,90) triangle

According Grossman Magnus's book the wall-paper figures are

present in the graphs which can completely cover the plane

by a fundamental region.

I have little experience with GAP too.

I know there's a GAP-package for crystallographic groups.

Now my question:

How can I identify or build the 17 groups by GAP?

Thank you very much in advance.

Giancarlo Bassi

g.bassi@tin.it

finger bassi@bellquel.scuole.bo.it

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