# Binary icosahedral group

From Encyclopedia of Mathematics

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

The group $\langle 5,3,2 \rangle$ abstractly presented as: $$ \langle A,B \ |\ A^5=B^3=(AB)^2 \rangle \ . $$ It is finite of order 120. It occurs as a subgroup of the unit quaternions.

The group has an action on the three-sphere with dodecahedral 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 icosahedral group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Binary_icosahedral_group&oldid=54413