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1
Symmetry Elements of the 2D Space Groups
glide line2, 3, 4, 6 – fold axes
Unit cell edgemirror line
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2
Highestorder
rotation
Has reflection?
Yes No
6-fold p6m p6
4-foldHas mirrors at 45°?
p4Yes: p4m No: p4g
3-foldHas rot. centre off mirrors?
p3Yes: p31m No: p3m1
2-fold
Has perpendicular reflections?Has glide reflection?
Yes No
Has rot. centre off mirrors?pmg Yes: pgg No: p2
Yes: cmm No: pmm
noneHas glide axis off mirrors? Has glide reflection?
Yes: cm No: pm Yes: pg No: p1
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Find the plane groups in the following 10 patterns marked in the yellow squares (for 1 and 2 the same pattern is shown more than once to help you in seeing/finding the plane group). Draw the unit cell in the each pattern and show the mirror and/or the glide lines accordingly.
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1. 1.
Pictures taken by Anke Zurn at Topkapi Palast, Istanbul
p4mm
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2.
2.
Pictures taken by Anke Zurn at Topkapi Palast, Istanbul
No mirrors!
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2.
Pictures taken by Anke Zurn at Topkapi Palast, Istanbul
p6 No mirrors!
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kiosk, close to TopkapiPalast;Istanbul, 2009
3.
p6mm
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Bamboo basket image source: http://www.fz-juelich.de (modified)
Basket waving: kagome net
4.p6
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Kagome network
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10
6.
p4
7.
p4gm
8.
p31m
9.
cmm2
10.
cm