Binary octahedral group

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