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

Author

Laith Rastanawi and Günter Rote, May 16 2022

Keywords

• nonn

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.