Namespaces
Variants
Actions

Binary octahedral group

From Encyclopedia of Mathematics
Revision as of 20:50, 23 November 2023 by Chapoton (talk | contribs) (→‎References: isbn link)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

2020 Mathematics Subject Classification: Primary: 20-XX [MSN][ZBL]

The group $\langle 4,3,2 \rangle$ abstractly presented as: $$ \langle A,B \ |\ A^4=B^3=(AB)^2 \rangle \ . $$ It is finite of order 48. It has the binary tetrahedral group $G_4 = \langle 3,3,2 \rangle$ as a subgroup of index 2. It occurs as a subgroup of the unit quaternions.

The group has an action on the three-sphere with octahedral space as quotient.

References

[1] H.S.M. Coxeter, "Regular complex polytopes", Cambridge Univ. Press (1991) pp. 77 ISBN 0-521-20125-X Zbl 0732.51002
How to Cite This Entry:
Binary octahedral group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Binary_octahedral_group&oldid=51429