Book Review
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Errata to “Crystallographic groups of four-dimensional space”:
Bull. Amer. Math. Soc. (N.S.), Volume 3, Number 1, Part 1 (1980), 777--777
MathSciNet review:
1567178
Full text of review:
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Book Information:
Authors:
Harold Brown,
Rolf Bülow,
Joachim Neubüser,
Hans Wondratschek and
Hans Zassenhaus
Title:
Crystallographic groups of four-dimensional space
Additional book information:
Wiley, New York, 1978, xiv + 443 pp., $38.90.
N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
J. J. Burckhardt, Der Briefwechsel von E. S. von Fedorow und A. Schoenflies, 1889–1908, Arch. History Exact Sci. 7 (1971), no. 2, 91–141 (German). MR 1554140, DOI 10.1007/BF00411807
H. S. M. Coxeter, Discrete groups generated by reflections, Ann. of Math. (2) 35 (1934), no. 3, 588–621. MR 1503182, DOI 10.2307/1968753
H. S. M. Coxeter, Regular and semi-regular polytopes. I, Math. Z. 46 (1940), 380–407. MR 2181, DOI 10.1007/BF01181449
H. S. M. Coxeter, Regular complex polytopes, Cambridge University Press, London-New York, 1974. MR 0370328
H. S. M. Coxeter [1978], Review of Three-dimensional nets and polyhedra, by A. F. Wells, Bull. Amer. Math. Soc. 84, 466-470.
Donald W. Crowe, The geometry of African art. I. Bakuba art, J. Geom. 1 (1971), 169–182. MR 490658, DOI 10.1007/BF02150270
Donald W. Crowe, The geometry of African art. I. Bakuba art, J. Geom. 1 (1971), 169–182. MR 490658, DOI 10.1007/BF02150270
Patrick Du Val, Homographies, quaternions and rotations, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0169108
E. S. Fedorov [1891], Zap. Imp. S. Petersburg Mineral. OBŠČ. (2) 28, 345-390.
L. Fejes Tóth, Regular figures, A Pergamon Press Book, The Macmillan Company, New York, 1964. MR 0165423
Leopold Flatto, Invariants of finite reflection groups, Enseign. Math. (2) 24 (1978), no. 3-4, 237–292. MR 519546
Ludwig Föppl [1914], Der Fundamentalbereich des Diamantgitters, Physikalische Z. 15, 191-193.
Michael Goldberg, On the space-filling heptahedra, Geom. Dedicata 7 (1978), no. 2, 175–184. MR 500559, DOI 10.1007/BF00181630
Caroline H. MacGillavry [1976], Fantasy and Symmetry-The periodic drawings of M. C. Escher, Abrams, New York.
Doris Schattschneider, The plane symmetry groups: their recognition and notation, Amer. Math. Monthly 85 (1978), no. 6, 439–450. MR 477980, DOI 10.2307/2320063
Doris Schattschneider, Tiling the plane with congruent pentagons, Math. Mag. 51 (1978), no. 1, 29–44. MR 493766, DOI 10.2307/2689644
W. Threlfall and H. Seifert, Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes, Math. Ann. 104 (1931), no. 1, 1–70 (German). MR 1512649, DOI 10.1007/BF01457920
- N. Bourbaki [1968], Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris. MR 0240238
- J. J. Burckhardt [1971], Der Briefwechsel von E. S. von Fedorow und A. Schoenflies, 1889-1908, Archive for History of Exact Sciences 7, 91-141. MR 1554140
- H. S. M. Coxeter [1934], Discrete groups generated by reflections, Ann. of Math. 35, 588-621. MR 1503182
- H. S. M. Coxeter [1940], Regular and semi-regular polytopes, Math. Z. 46, 380-407. MR 2181
- H. S. M. Coxeter [1974], Regular complex polytopes, Cambridge Univ. Press, London and New York. MR 370328
- H. S. M. Coxeter [1978], Review of Three-dimensional nets and polyhedra, by A. F. Wells, Bull. Amer. Math. Soc. 84, 466-470.
- D. W. Crowe [1971], The geometry of African art: I, J. Geometry 1, 169-182. MR 490658
- D. W. Crowe [1975], The geometry of African art: II, Historia Math. 2, 253-271. MR 490659
- Patrick DuVal [1964], Homographies, quaternions and rotations, Clarendon Press, Oxford. MR 169108
- E. S. Fedorov [1891], Zap. Imp. S. Petersburg Mineral. OBŠČ. (2) 28, 345-390.
- L. Fejes Tóth [1964], Regular figures, Pergamon Press, New York. MR 165423
- Leopold Flatto [1978], Invariants of finite reflection groups, L'Enseignement Math. (2) 24, 237-292. MR 519546
- Ludwig Föppl [1914], Der Fundamentalbereich des Diamantgitters, Physikalische Z. 15, 191-193.
- Michael Goldberg [1978], On the space-filling heptahedra, Geometriae Dedicata 7, 175-184. MR 500559
- Caroline H. MacGillavry [1976], Fantasy and Symmetry-The periodic drawings of M. C. Escher, Abrams, New York.
- Doris Schattschneider [1978a], The plane symmetry groups: their recognition and notation, Amer. Math. Monthly 85, 439-450. MR 477980
- Doris Schattschneider [1978b], Tiling the plane with congruent pentagons, Math. Magazine 51, 29-44. MR 493766
- W. Threlfall and H. Seifert [1931], Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen der driedimensionalen sphärischen Raumes, Math. Ann. 104, 1-70. MR 1512649
Review Information:
Reviewer:
H. S. M. Coxeter
Journal:
Bull. Amer. Math. Soc.
1 (1979), 792-794
DOI:
https://doi.org/10.1090/S0273-0979-1979-14673-1
