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Listing the elements of a symmetry group of a frieze pattern 
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#1
Apr1611, 03:01 PM

P: 12

I have run into a problem where I have a frieze pattern F, the frieze pattern has horizontal refelctive symmetry, glide reflective symmetry, but does not have 180 degree rotation and does not have vertical reflective symmetry.
G represents the symmetry group for F. G={reflection symmetry, translational symmetry} and the mirror of the reflection is parallel to the vector of the translation. Hence a glide reflection with the translation composed with the reflection. I now have to list the elements of G, not exactly sure what to do at that point. Can anybody help me out? 


#2
Apr1811, 11:29 PM

Sci Advisor
P: 906

this sounds like the "jump" frieze group, which is isomorphic to Z x Z2, and generated by
the horizontal translation (1,0) and the horizontal reflection (0,1). a glide reflection is of the form (k,1). as with any frieze group it is infinite, but we have basically 4 types of symmetries: (k,0), a translation (k,1), a glide reflection (0,1), the horizontal reflection (0,0), the identity. 


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