The icosahedral group I is the group of 60 rotational symmetries of a dodecahedron. A diagonal of the dodecahedron is a segment joining opposite vertices. There are 10 such diagonals. How many rotations of I are in the stabilizer of a diagonal? (You do not need to describe them, just figure out their number.) Justify your answer using group actions and the counting formula.

The icosahedral group I is the group of 60 rotational symmetries of a dodecahedron. A diagonal of the dodecahedron is a segment joining opposite vertices. There are 10 such diagonals. How many rotations of I are in the stabilizer of a diagonal? (You do not need to describe them, just figure out their number.) Justify your answer using group actions and the counting formula.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 10E: Exercises 10. Find an isomorphism from the multiplicative group to the group with multiplication...

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