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References and Notes

1. An annotated collection of these prints can be found in Macgillavry, C. H., Symmetry Aspects of M. C. Escher's Periodic Drawings , International Union of Crystallography (1965).

2. The use of Arabic geometrical patterns in crystallographic teaching has been discussed by E. and M. Makovicky in N. Jb. Miner. Mh ., 1977, 58-68. Numerous illustrations can be found in a book by J. Bourgoin (Arabic Pattern and Design , originally published in 1879 (in French) and reprinted without text by Dover in 1973).

3. The back side of a stamp sheet displays a higher symmetry for it shows the lattice only and not the structure.

4. cf. Bloss, F. D., Crystallography and Crystal Chemistry , Holt, Rinehart and Winston (1971); Buerger, M. J., Elementary Crystallography , Wiley (1963); Dent Glasser, L. S., Crystallography and its Applications , Van Nostrand Reinhold (1977); Megaw, H. D., Crystal Structures: A Working Approach , Saunders (1973).

5. International Tables for X-ray Crystallography Vol. I (1952).

6. Sands, D. E., Introduction to Crystallography . Benjamin (1969).

7. The two patterns (iv) and (v) can indeed serve to illustrate various aspects of a subgroup relation.

8. A set of worksheets comprising additional space groups can be obtained from the author (Prof. W. M. Meier, Institute of Crystallography and Petrography, ETH, 8092 Zurich, Switzerland).

Plate (i) to (xv). Worksheets for practical exercises.

Select thumbnail for large (1280x888 pixels, typically 20kB) image.

Plate i	Plate ii	Plate iii	Plate iv
Plate v	Plate vi	Plate vii	Plate viii
Plate ix	Plate x	Plate xi	Plate xii
Plate xiii	Plate xiv	Plate xv

List of space groups represented in plates (i) to (xv)

(i) Pma2 (plane group pmg)

(ii) Pnc2

(ii) Pbn2₁

(iv) Cc

(v) Cmc2₁

(vi) Aba2

(vii) Pnn2

(viii) P2₁22

(ix) P31c

(x) Pban

(xi) $P\overline{4}2_1m$

(xii) P4/nbm

(xiii) $P\overline{4}b2$

(xiv) $P\overline{4}2m$

(xv) $P\overline{4}m2$

Space group of structure in Fig. 4: Pbn2₁.

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