symmetry elements of the 2d space groupsn.ethz.ch/~nielssi/download/4. semester/ac ii/uebungen...1...

1

Symmetry Elements of the 2D Space Groups

glide line2, 3, 4, 6 – fold axes

Unit cell edgemirror line

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

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.

1. 1.

Pictures taken by Anke Zurn at Topkapi Palast, Istanbul

p4mm

2.

2.

Pictures taken by Anke Zurn at Topkapi Palast, Istanbul

No mirrors!

2.

Pictures taken by Anke Zurn at Topkapi Palast, Istanbul

p6 No mirrors!

kiosk, close to TopkapiPalast;Istanbul, 2009

3.

p6mm

Bamboo basket image source: http://www.fz-juelich.de (modified)

Basket waving: kagome net

4.p6

Kagome network

10

6.

p4

7.

p4gm

8.

p31m

9.

cmm2

10.

cm