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Difference between revisions of "Binary octahedral group"

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<TR><TD valign="top">[1]</TD> <TD valign="top"> H.S.M. Coxeter,   "Regular complex polytopes" , Cambridge Univ. Press (1991) pp. 77 ISBN 0-521-20125-X  {{ZBL|0732.51002}}</TD></TR>
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<TR><TD valign="top">[1]</TD> <TD valign="top"> H.S.M. Coxeter, "Regular complex polytopes", Cambridge Univ. Press (1991) pp. 77 {{ISBN|0-521-20125-X}} {{ZBL|0732.51002}}</TD></TR>
 
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Latest revision as of 20:50, 23 November 2023

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=54643