A354046 Number of 4-dimensional chiral point groups of order n.

1, 2, 3, 6, 4, 10, 5, 17, 8, 14, 7, 27, 8, 18, 14, 37, 10, 31, 11, 36, 18, 26, 13, 71, 17, 30, 22, 46, 16, 56, 17, 73, 26, 38, 26, 78, 20, 42, 30, 86, 22, 72, 23, 66, 42, 50, 25, 147, 30, 67, 38, 76, 28, 88, 38, 108, 42, 62, 31, 142, 32, 66, 55, 134, 44

Offset

1,2

Comments

In other words, the number of (finite) subgroups of order n of the special orthogonal group SO(4).

References

John H. Conway and Derek A. Smith, On Quaternions and Octonions, CRC Press, 2003.

Patrick Du Val, Homographies, Quaternions and Rotations. Clarendon Press, 1964.

Links

Laith Rastanawi and Günter Rote, Table of n, a(n) for n = 1..10000

Edouard Goursat, Sur les substitutions orthogonales et les divisions régulières de l'espace, Annales scientifiques de l'E.N.S. 3e série, 6:9-102, 1889.

A. C. Hurley, Finite rotation groups and crystal classes in four dimensions, Mathematical Proceedings of the Cambridge Philosophical Society, 47(4):650-661, 1951.

Laith Rastanawi and Günter Rote, Towards a Geometric Understanding of the 4-Dimensional Point Groups, arXiv preprint arXiv:2205.04965 [math.MG], 2022.

Laith Rastanawi and Günter Rote, Sage code used to generate the sequence.

W. Threlfall and H. Seifert, Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes, Math. Annalen, 104:1-70, 1931.

W. Threlfall and H. Seifert, Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes (Schluß), Math. Annalen, 107:543-586, 1933.

Crossrefs

Cf. A353341.

Sequence in context: A363444 A194357 A165783 * A368275 A289272 A073318

Adjacent sequences: A354043 A354044 A354045 * A354047 A354048 A354049

Keyword

nonn

Author

Laith Rastanawi and Günter Rote, May 16 2022

Status

approved