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A004028 Number of geometric n-dimensional crystal classes.
(Formerly M1965)
1, 2, 10, 32, 227, 955, 7103 (list; graph; refs; listen; history; text; internal format)



Number of Q-classes of finite subgroups of GL_n(Z) up to conjugacy.

Number of n-dimensional crystallographic point groups (not counting enantiomorphs). - Andrey Zabolotskiy, Jul 08 2017


H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.

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.

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]

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

E. S. Rosenthal & N. J. A. Sloane, Correspondence, 1975


Cf. A004027, A004029.

Sequence in context: A032095 A264960 A151019 * A263839 A236921 A080668

Adjacent sequences:  A004025 A004026 A004027 * A004029 A004030 A004031




N. J. A. Sloane


a(6) corrected from CARAT page by D. S. McNeil, Jan 02 2011



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Last modified November 21 10:02 EST 2017. Contains 295000 sequences.