A004028 Number of geometric n-dimensional crystal classes.

1, 2, 10, 32, 227, 955, 7103

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice
• more

Comments

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

References

• 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).

Links

• 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.

Crossrefs

Cf. A004027, A004029.

Extensions

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