Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 3 / 8D / b / ii

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- Solution ii

Solution

There are twelve edges and the action on them is transitive, so an edge stabilizer has order

\frac{48}{12} = 4.

For an edge parallel to the

z

-axis with midpoint

(1, 1, 0)

, its stabilizer is generated by interchanging

x

and

y

and by replacing

z

by

- z

. These are commuting involutions, so

G_{e} ≅ C_{2} \times C_{2} .

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