Listing the elements of a symmetry group of a frieze pattern

JohnMcBetty

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?

Deveno

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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Deveno Recognitions: Science Advisor	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.