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A006226 Number of abstract n-dimensional crystallographic point groups.
(Formerly M1916)
1, 2, 9, 18, 118, 239, 1594 (list; graph; refs; listen; history; text; internal format)



P. Engel, "Geometric crystallography," in P. M. Gruber and J. M. Wills, editors, Handbook of Convex Geometry. North-Holland, Amsterdam, Vol. B, pp. 989-1041.

T. Janssen, Crystallographic Groups. North-Holland, Amsterdam, 1973, p. 73.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=0..6.

A. C. Hurley, Finite rotation groups and crystal classes in four dimensions, Proc. Cambridge Philos. Soc. 47, (1951). 650-661.

A. C. Hurley, Crystal Classes of Four-Dimensional Space R4, Acta Crystallog., 22 (1967), see especially p. 605.

W. Plesken and T. Schulz, Counting crystallographic groups in low dimensions, Experimental Mathematics, 9 (No. 3, 2000), 407-411.

W. Plesken and T. Schulz, CARAT Homepage

W. Plesken and T. Schulz, CARAT Homepage [Cached copy in pdf format (without subsidiary pages), with permission]

W. Plesken and T. Schulz, Introduction to CARAT [Cached copy in pdf format (without subsidiary pages), with permission]


Cf. A004027, A004028, A004029.

Sequence in context: A037421 A083423 A068978 * A109298 A075537 A180852

Adjacent sequences:  A006223 A006224 A006225 * A006227 A006228 A006229




N. J. A. Sloane


Two more terms from W. Plesken and T. Schulz (tilman(AT)momo.math.rwth-aachen.de), Feb 27 2001

Offset corrected by Andrey Zabolotskiy, Jul 10 2017



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Last modified August 18 23:38 EDT 2017. Contains 290781 sequences.