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Rotation Groups and Permutation Groups

Published online by Cambridge University Press:  03 November 2016

A. W Fuller
A. W Fuller*
Affiliation:
Barley Hill, Watledge, Nailsworth, Glos
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Extract

Several books on Group Theory show that the isomorphism between the group of proper rotations of a cube and P4, the group of 24 permutations on four arbitrary symbols, can be established by a consideration of the four diagonals of the cube. To each arrangement of these diagonals corresponds a unique position of the cube and therefore a unique rotation from one position as reference to that position. The extension of this result to other polyhedra does not appear in the books that I know.

Type
Research Article
Information
The Mathematical Gazette , Volume 47 , Issue 361 , October 1963 , pp. 209 - 210
Copyright
Copyright © Mathematical Association 1963

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References

page 209 note * Dr. Cundy has pointed out that the result for the dodecahedron is illustrated on page 35 of Coxeter and Moser: “Generators and Relations for Discrete Groups.”