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Dodecahedron problem irreducible

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Consider the action of the group A_5 on the faces of a dodecahedron. Decompose the corresponding representation of A_5 into a sum of irreducibles and solve the problem by diagonilizing the interwining operator.

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This shows how to decompose a representation of a group into a sum of irreducibles.

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Dodecahedron problem A_5 irreducibles

Consider the action of the group A_5 on the faces of a dodecahedron.
Decompose the corresponding representation of A_5 into a sum of
irreducibles and solve the problem by diagonalizing the interwining operator.

Solution: A dodecahedron has 12 faces with 20 vertices. The rotational group is the permutation group A5 and the symmetric groups is A5 x Z2, that is a subgroup of S20 (since it has 20 ...

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